PHYSICS FOR NEET

EXERCISE-1

Q.1 Two metallic spheres of same mass are given equal and opposite charges; then :

(1) the mass of positively charged sphere increases

(2) the mass of both remains the same

(3) the mass of negatively charged sphere increases

(4) the mass of both spheres increase

Q.2 Which one of the following statement regarding electrostatics is wrong ?

(1) Charge is quantized

(2) Charge is conserved

(3) There is an electric field near an isolated charge at rest

(4) A stationary charge produces both electric and magnetic fields

Q.3 Two identical metallic sphere are charged with 10 and \(-20\) units of charge. If both the spheres are first brought into contact with each other and then are placed to their previous positions, then the ratio of the force in the two situations will be :-

(1) \(8: 1\)

(2) \(1: 8\)

(3) \(2: 1\)

(4) \(1: 2\)

Q.4 A stationary electric charge produces-

(1) Only electric fields

(2) Only magnetic field

(3) Both electric as magnetic field

(4) Neither electric Nor magnetic field

Q.5 It is observed that when a soap bubble is given some positive charge its radius increases. What will happen to the same soap bubble if it is given equal negative charge instead of positive charge?

(1) Its radius increases

(2) Its radius decreases

(3) Its radius remains same

(4) It gets burst

Q.6 Two charges placed in air repel each other by a force of \(10^{-4} \mathrm{~N}\). When oil is introduced between the charges, the force becomes \(2.5 \times 10^{-5} \mathrm{~N}\). The dielectric constant of oil is :

(1) \(2.5\)

(2) \(0.25\)

(3) \(2.0\)

(4) \(4.0\)

Q.7 The ratio of the forces between two small spheres with constant charges (a) in air and (b) in a medium of dielectric constant \(\mathrm{K}\) is respectively:

(1) \(1: \mathrm{K}\)

(2) \(\mathrm{K}: 1\)

(3) \(1: \mathrm{K}^{2}\)

(4) \(\mathrm{K}^{2}: 1\)

Q.8 Two charges of \(+1 \mu \mathrm{C} \&+5 \mu \mathrm{C}\) are placed \(4 \mathrm{~cm}\) apart, the ratio of the force exerted by both charges on each other will be -

(1) \(1: 1\)

(2) \(1: 5\)

(3) \(5: 1\)

(4) \(25: 1\)

Q.9 The force between two point charges in vacuum is \(15 \mathrm{~N}\), if a brass plate is introduced between the two charges, then force between them will-

(1) Becomes zero

(2) Remains the same

(3) Becomes \(30 \mathrm{~N}\)

(4) Becomes \(60 \mathrm{~N}\) 

\section{ELECTROSTATICS}

Q.10 The force between two point charges placed in vacuum at distance \(1 \mathrm{~mm}\) is \(18 \mathrm{~N}\). If a glass plate of thickness \(1 \mathrm{~mm}\) and dielectric constant 6 , be kept between the charges then new force between them would be-

(1) \(18 \mathrm{~N}\)

(2) \(108 \mathrm{~N}\)

(3) \(3 \mathrm{~N}\)

(4) \(3 \times 10^{-6} \mathrm{~N}\)

Q.11 Five point charges, each of value \(+\mathrm{q}\) Coulomb, are placed on five vertices of a regular hexagon of side L metre. The magnitude of the force on a point charge of value -q Coulomb placed at the centre of the hexagon is -

(1) \(\frac{\mathrm{kq}^{2}}{\mathrm{~L}^{2}}\)

(2) \(\sqrt{5} \frac{\mathrm{kq}^{2}}{\mathrm{~L}^{2}}\)

(3) \(\sqrt{3} \frac{\mathrm{kq}^{2}}{\mathrm{~L}^{2}}\)

(4) Zero

Q.12 A body has 80 microcoulomb of charge. Number of additional electrons on it will be :

(1) \(8 \times 10^{-5}\)

(2) \(80 \times 10^{15}\)

(3) \(5 \times 10^{14}\)

(4) \(1.28 \times 10^{-17}\)

Q.13 A pendulem bob of mass \(80 \mathrm{mg}\) and carrying a charge of \(2 \times 10^{-8}\) Coulomb is at rest in a horizontal uniform electric field of \(20,000 \mathrm{~V} \mathrm{~m}^{-1}\). Find the tension in the thread of pendulum -

(1) \(8.8 \times 10^{-2} \mathrm{~N}\)

(2) \(8.8 \times 10^{-3} \mathrm{~N}\)

(3) \(8.8 \times 10^{-4} \mathrm{~N}\)

(4) \(8.8 \times 10^{-5} \mathrm{~N}\)

Q.14 Four equal but like charge are placed at four corners of a square. The electric field intensity at the center of the square due to any one charge is \(E\), then the resultant electric field intensity at centre of square will be :

(1) Zero

(2) \(4 \mathrm{E}\)

(3) \(E\)

(4) \(1 / 2 \mathrm{E}\)

Q.15 Three charge \(+4 \mathrm{q}, \mathrm{Q}\) and \(\mathrm{q}\) are placed in a straight line of length \(\ell\) at points distance \(0, \ell / 2\) and \(\ell\) respectively. What should be the value of \(\mathrm{Q}\) in order to make the net force on \(\mathrm{q}\) to be zero?

(1) \(-\mathrm{q}\)

(2) \(-2 q\)

(3) \(-q / 2\)

(4) \(4 \mathrm{q}\)

Q.16 Two point charges placed at a distance \(r\) in air exert a force \(F\) on each other. The value of distance \(\mathrm{R}\) at which they experience force \(4 \mathrm{~F}\) when placed in a medium of dielectric constant \(\mathrm{K}=16\) is :

(1) \(r\)

(2) \(r / 4\)

(3) \(r / 8\)

(4) \(2 r\)

Q.17 Four charges \(+\mathrm{q},+\mathrm{q},-\mathrm{q}\) and \(-\mathrm{q}\) are placed respectively at the corners \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and D of a square of side "a", arranged in the given order. Calculate the intensity at \((\mathrm{O})\) the centre of the square

(1) \(\frac{4 \pi \varepsilon_{0} \cdot a^{2}}{4 \sqrt{2} q}\)

(2) \(\frac{4 \sqrt{2} q}{4 \pi \varepsilon_{0} \cdot a^{2}}\)

(3) \(\frac{\pi \varepsilon_{0} \cdot a^{2}}{4 \sqrt{2} q}\)

(4) \(\frac{4 \sqrt{2} q}{\pi \varepsilon_{0} \cdot a^{2}}\)

Q.18 Four charges are arranged at the corners of a square \(\mathrm{ABCD}\), as shown. The force on a +ve charge kept at the centre of the square is

(1) zero

(2) along diagonal \(\mathrm{AC}\)

(3) along diagonal BD

(4) perpendicular to the side \(\mathrm{AB}\)


\section{ELECTROSTATICS}

Q.19 Three identical charges each of \(1 \mu \mathrm{C}\) are kept on the circumference of a circle of radius 1 metre forming equilateral triangle. The electric intensity at the center of the circle in \(\mathrm{N} / \mathrm{C}\) is

(1) \(9 \times 10^{3}\)

(2) \(13.5 \times 10^{3}\)

(3) \(27 \times 10^{3}\)

(4) Zero

Q.20 The three charges each of \(5 \times 10^{-6}\) coulomb are placed at vertex of an equilateral triangle of side \(10 \mathrm{~cm}\). The force exerted on the charge of \(1 \mu \mathrm{C}\) placed at centre of triangle in newton will be

(1) \(13.5\)

(2) zero

(3) \(4.5\)

(4) \(6.75\)

Q.21 Four equal charges, each \(+\mathrm{q}\) are placed at the corners of a square of side a. Then the coulomb force experienced by one charge due to the rest of three is :

(1) \((2 \sqrt{2}+1) \mathrm{Kq}^{2} / 2 \mathrm{a}^{2}\)

(2) \(3 \mathrm{Kq}^{2} / \mathrm{a}^{2}\)

(3) \(2 \sqrt{2} \mathrm{Kq}^{2} / \mathrm{a}^{2}\)

(4) zero

Q.22 Six charges \(+Q\) each are placed at the corners of a regular hexagon of side (a), the electric field at the centre of hexagon is-

(1) Zero

(2) \(\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{6 Q^{2}}{a^{2}}\)

(3) \(\frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q^{2}}{a^{2}}\)

(4) \(\frac{1}{4 \pi \in_{0}} \cdot \frac{6 Q^{2}}{a \sqrt{2}}\)

Q.23 Two free positive charges \(4 \mathrm{q}\) and \(\mathrm{q}\) are a distance \(l\) apart. What charge \(\mathrm{Q}\) is needed to achieve equilibrium for the entire system and where should it be placed form charge \(q\) ?

(1) \(\mathrm{Q}=\frac{4}{9} \mathrm{q}\) (negative) at \(\frac{l}{3}\)

(2) \(\mathrm{Q}=\frac{4}{9} \mathrm{q}\) (positive) at \(\frac{l}{3}\)

(3) \(\mathrm{Q}=\mathrm{q}\left(\right.\) positive) at \(\frac{l}{3}\)

(4) \(\mathrm{Q}=\mathrm{q}\) (negative) at \(\frac{l}{3}\)

Q.24 Six charges are placed at the corner of a regular hexagon as shown. If an electron is placed at its centre \(\mathrm{O}\), force on it will be:

(1) Zero

(3) Along OC

(2) Along OF

(4) None of these


\section{ELECTRIC FIELD}

Q.25 Three charges \(+3 \mathrm{q},+\mathrm{q}\) and \(\mathrm{Q}\) are placed on a straight line with equal separation . In order to make the net force on \(q\) to be zero, the value of \(Q\) will be

(1) \(+3 q\)

\((2)+2 q\)

(3) \(-3 q\)

(4) \(-4 \mathrm{q}\)

Q.26 Two parallel large thin metal sheets have equal surface charge densities \(\left(\sigma=26.4 \times 10^{-12} \mathrm{c} / \mathrm{m}^{2}\right)\) of opposite signs. The electric field between these plates is :

(1) \(1.5 \mathrm{~N} / \mathrm{C}\)

(2) \(1.5 \times 10^{-10} \mathrm{~N} / \mathrm{C}\)

(3) \(3 \mathrm{~N} / \mathrm{C}\)

(4) \(3 \times 10^{-10} \mathrm{~N} / \mathrm{C}\)

Q.27 If an electron is placed in a uniform electric field, then the electron will :

(1) experience no force.

(2) moving with constant velocity in the direction of the field.

(3) move with constant velocity in the direction opposite to the field.

(4) accelerate in direction opposite to field. 

\section{ELECTROSTATICS}

Q.28 If \(\mathrm{Q}=2\) coloumb and force on it is \(\mathrm{F}=100\) newton, then the value of field intensity will be:

(1) \(100 \mathrm{~N} / \mathrm{C}\)

(2) \(50 \mathrm{~N} / \mathrm{C}\)

(3) \(200 \mathrm{~N} / \mathrm{C}\)

(4) \(10 \mathrm{~N} / \mathrm{C}\)

Q.29 The electric field intensity due to a uniformly charged sphere is zero :

(1) at the centre

(2) at infinity

(3) at the centre and at infinite distance

(4) on the surface

Q.30 Two spheres of radii \(2 \mathrm{~cm}\) and \(4 \mathrm{~cm}\) are charged equally, then the ratio of charge density on the surfaces of the spheres will be -

(1) \(1: 2\)

(2) \(4: 1\)

(3) \(8: 1\)

(4) \(1: 4\)

Q.31 A charged water drop of radius \(0.1 \mu \mathrm{m}\) is under equilibrium in some electric field. The charge on the drop is equivalent to electronic charge. The intensity of electric field is \(\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\) -

(1) \(1.61 \mathrm{NC}^{-1}\)

(2) \(26.2 \mathrm{NC}^{-1}\)

(3) \(262 \mathrm{NC}^{-1}\)

(4) \(1610 \mathrm{NC}^{-1}\)

Q.32 Two large sized charged plates have a charge density of \(+\sigma\) and \(-\sigma\). The resultant force on the proton located midway between them will be -

(1) \(\sigma \mathrm{e} / \epsilon_{0}\)

(2) \(\sigma \mathrm{e} / 2 \epsilon_{0}\)

(3) \(2 \sigma e / \epsilon_{0}\)

(4) zero

Q.33 There is a uniform electric field in \(\mathrm{x}\)-direction. If the work done by external agent in moving a charge of \(0.2 \mathrm{C}\) through a distance of 2 metre slowly along the line making an angle of \(60^{\circ}\) with \(\mathrm{x}\)-direction is 4 joule, then the magnitude of \(\mathrm{E}\) is:

(1) \(\sqrt{3} \mathrm{~N} / \mathrm{C}\)

(2) \(4 \mathrm{~N} / \mathrm{C}\)

(3) \(5 \mathrm{~N} / \mathrm{C}\)

(4) \(20 \mathrm{~N} / \mathrm{C}\)

Q.34 A simple pendulum has a length \(\ell\), mass of bob \(\mathrm{m}\). The bob is given a charge q coulomb. The pendulum is suspended in a uniform horizontal electric field of strength \(E\) as shown in figure, then calculate the time period of oscillation when the bob is slightly displace from its mean position is :


(1) \(2 \pi \sqrt{\frac{\ell}{g}}\)

(2) \(2 \pi \sqrt{\left\{\frac{\ell}{g+\frac{q E}{m}}\right\}}\)

(3) \(2 \pi \sqrt{\left\{\frac{\ell}{g-\frac{q E}{m}}\right\}}\)


\section{ELECTROSTATICS}

Q.35 A charged particle of charge \(\mathrm{q}\) and mass \(\mathrm{m}\) is released from rest in an uniform electric field E. Neglecting the effect of gravity, the kinetic energy of the charged particle after time ' \(\mathrm{t}\) ' seconds is

(1) \(\frac{\text { Eqm }}{t}\)

(2) \(\frac{E^{2} q^{2} t^{2}}{2 m}\)

(3) \(\frac{2 E^{2} t^{2}}{m q}\)

(4) \(\frac{E q^{2} m}{2 t^{2}}\)

Q.36 Five balls, numbered 1 to 5, are suspended using separate threads. Pairs \((1,2),(2,4),(4,1)\) show electrostatic attraction, while pairs \((2,3)\) and \((4,5)\) show repulsion. Therefore ball 1 :

(1) Must be positively charged

(2) Must be negatively charged

(3) May be neutral

(4) Must be made of metal

Q.37 The electric field above a uniformly charged nonconducting sheet is E. If the nonconducting sheet is now replaced by a conducting sheet, with the charge same as before, the new electric field at the same point is :

(1) \(2 \mathrm{E}\)

(2) \(\mathrm{E}\)

(3) \(\frac{E}{2}\)

(4) None of these

Q.38 A positively charged pendulum is oscillating in a uniform electric field as shown in Figure. Its time period of SHM as compared to that when it was uncharged. \((\mathrm{mg}>\mathrm{qE})\)

(1) Will increase

(2) Will decrease

(3) Will not change

(4) Will first increase then decrease


Q.39 Two small spherical balls each carrying a charge \(\mathrm{Q}=10 \mu \mathrm{C}(10\) micro-coulomb \()\) are suspended by two insulating threads of equal lengths 1 each, from a point fixed in the ceiling. If is found that is equilibrium threads are separated by an angle \(60^{\circ}\) between them, as shown in the fig. What is the tension in the threads (Given \(\left.\frac{1}{\left(4 \pi \varepsilon_{0}\right)}=9 \times 10^{9} \mathrm{Nm} / \mathrm{C}^{2}\right)\) -


(1) \(18 \mathrm{~N}\)

(2) \(1.8 \mathrm{~N}\)

(3) \(0.18 \mathrm{~N}\)

(4) none of the above

Q.40 Two spheres of equal mass \(\mathrm{A}\) and \(\mathrm{B}\) are given \(+\mathrm{q}\) and \(-\mathrm{q}\) charge respectively then -

(1) mass of A increases

(2) mass of B increases

(3) mass of A remains constant

(4) mass of B decreases 

\section{ELECTROSTATICS}

Q.41 The wrong statement about electric lines of force is -

(1) These originate from positive charge and end on negative charge

(2) they do no intersect each other at a point

(3) they have the same form for a point charge and a sphere

(4) they have physical existences

Q.42 Choose correct statement regarding electric lines of force :

(1) emerges from (-ve) charge and meet from (+ve) charge

(2) where the electric lines of force are close electic field in that region is strong

(3) just as it is shown for a point system in the same way it represent for a solid sphere

(4) has a physical nature

Q.43 The electric field required to keep a water drop of mass \(\mathrm{m}\) and charge e just to remain suspended is :

(1) \(\mathrm{mg}\)

(2) emg

(3) \(\frac{m g}{e}\)

(4) \(\frac{e m}{g}\)

Q.44 The separation between the two charges \(+q\) and \(-q\) becomes double. The value of force will be :

(1) two fold

(2) half

(3) four fold

(4) one fourth

Q.45 When a glass rod is rubbed with silk, the amount of positive charge acquired by glass rod in magnitude is:

(1) less than the charge on silk

(2) greater than the charge on slik

(3) equal to the charge on silk

(4) none of these

Q.46 The dielectric constant \(\mathrm{K}\) of an insulator can be :

(1) 5

(2) \(0.5\)

(3) \(-1\)

(4) zero

Q.47 A cube has point charges of magnitude - \(\mathrm{q}\) at all its vertices. Electric field at the centre of the cube is :

(1) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{6 q}{3 a^{2}}\)

(2) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{8 q}{a^{2}}\)

(3) zero

(4) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{-8 q}{a^{2}}\)

Q.48 A charged oil drop is suspended in uniform field of \(3 \times 10^{4} \mathrm{~V} / \mathrm{m}\) so that it neither falls nor rises. The charge on the drop will be (Take the mass of the drop \(=9.9 \times 10^{-15} \mathrm{~kg}\) and \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\) )

(1) \(3.3 \times 10^{-18} \mathrm{C}\)

(2) \(3.2 \times 10^{-18} \mathrm{C}\)

(3) \(1.6 \times 10^{-18} \mathrm{C}\)

(4) \(4.8 \times 10^{-18} \mathrm{C}\)

Q.49 Two particle of equal mass \(m\) and charge \(q\) are placed at a distance of \(16 \mathrm{~cm}\). Net force on each charge is zero then value of \(\frac{\mathrm{q}}{\mathrm{m}}\) is

(1) 1

(2) \(\sqrt{\frac{\pi \varepsilon_{0}}{G}}\)

(3) \(\sqrt{\frac{\mathrm{G}}{4 \pi \varepsilon_{0}}}\)

(4) \(\sqrt{4 \pi \varepsilon_{0} G}\)

Q.50 An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The Coulomb force \(\overrightarrow{\mathrm{F}}\) on the electron is :

(1) \(\mathrm{K} \frac{\mathrm{e}^{2}}{\mathrm{r}^{2}} \hat{\mathrm{r}}\)

(2) \(-\mathrm{K} \frac{\mathrm{e}^{2}}{\mathrm{r}^{3}} \hat{\mathrm{r}}\)

(3) \(\mathrm{K} \frac{\mathrm{e}^{2}}{\mathrm{r}^{3}} \overrightarrow{\mathrm{r}}\)

(4) \(-\mathrm{K} \frac{\mathrm{e}^{2}}{\mathrm{r}^{3}} \overrightarrow{\mathrm{r}}\) 

\section{ELECTROSTATICS}

Q.51 Two positive charges of \(1 \mu \mathrm{C}\) and \(2 \mu \mathrm{C}\) are placed 1 metre apart. The value of electric field in N/ \(\mathrm{C}\) at the middle point of the line joining the charges will be :-

(1) \(10.8 \times 10^{4}\)

(2) \(3.6 \times 10^{4}\)

(3) \(1.8 \times 10^{4}\)

(4) \(5.4 \times 10^{4}\)

Q.52 Which one of the following pattern of electric line of force can't possible :-

(1)


\((2)\)


(3)


(4)


\section{FLUX CALUCULATION AND GAUSS LAW :}

Q.53 How much electric flux will come out through a surface of area vector \(\overrightarrow{\mathrm{S}}=10 \hat{\mathrm{j}}\) kept in an electrostatic field \(E=2 \hat{i}+4 \hat{j}+3 \hat{k}\) ?

(1) 20 units

(2) 40 units

(3) 30 units

(4) 90 units

Q.54 Flux coming out from a unit positive charge placed in air and enclosed by a surface is :

(1) \(\varepsilon_{0}\)

(2) \(\varepsilon_{0}^{-1}\)

(3) \(\left(4 \pi \varepsilon_{0}\right)^{-1}\)

(4) \(4 \pi \varepsilon_{0}\)

Q.55 The flux entering and leaving a closed surface are \(5 \times 10^{5}\) and \(4 \times 10^{5} \mathrm{MKS}\) units respectively; then the charge inside the surface will be :

(1) \(-8.85 \times 10^{-7} \mathrm{C}\)

(2) \(8.85 \times 10^{-7} \mathrm{C}\)

(3) \(8.85 \times 10^{7} \mathrm{C}\)

(4) \(6.85 \times 10^{-7} \mathrm{C}\)

Q.56 In a region of space the electric field is given by \(\overrightarrow{\mathrm{E}}=8 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\). The electric flux through a surface of area of 100 units in x-y plane is :

(1) 800 units

(2) 300 units

(3) 400 units

(4) 1500 units

Q.57 Three charges \(\mathrm{q}_{1}=1 \mu \mathrm{c}, \mathrm{q}_{2}=2 \mu \mathrm{c}\) and \(\mathrm{q}_{3}=-3 \mu \mathrm{c}\) and four surfaces \(\mathrm{S}_{1}, \mathrm{~S}_{2}, \mathrm{~S}_{3}\) and \(\mathrm{S}_{4}\) are shown. The flux emerging through surface \(\mathrm{S}_{2}\) in \(\mathrm{N}-\mathrm{m}^{2} / \mathrm{C}\) is -

(1) \(36 \pi \times 10^{3}\)

(2) \(-36 \pi \times 10^{3}\)

(3) \(36 \pi \times 10^{9}\)

(4) \(-36 \pi \times 10^{9}\)


Q.58 Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius \(10 \mathrm{~cm}\) surrounding the total charge is \(25 \mathrm{~V}-\mathrm{m}\). The flux over a concentricsphere of radius \(20 \mathrm{~cm}\) will be :-

(1) \(25 \mathrm{~V}-\mathrm{m}\)

(2) \(50 \mathrm{~V}-\mathrm{m}\)

(3) \(100 \mathrm{~V}-\mathrm{m}\)

(4) \(200 \mathrm{~V}-\mathrm{m}\)

Q.59 A charge \(q\) is placed at the centre of the open end of a cylindrical vessel figure. The flux of the electric field through the surface of the vessel is :-

(1) zero

(2) \(\mathrm{q} / \varepsilon_{0}\)

(3) \(\mathrm{q} / 2 \varepsilon_{0}\)

(4) \(2 q / \varepsilon_{0}\) 

\section{ELECTROSTATICS}

Q.60 In a certain region of surface there exists a uniform electric field of \(2 \times 10^{3} \hat{\mathrm{k}} \mathrm{V} / \mathrm{m}\). A rectangular coil of dimensions \(10 \mathrm{~cm} \times 20 \mathrm{~cm}\) is placed in x-y plane. The electric flux through the coil is -

(1) zero

(2) \(4 \times 10^{-3} \mathrm{~V}-\mathrm{m}\)

(3) \(40 \mathrm{~V}-\mathrm{m}\)

(4) \(4 \times 10^{5} \mathrm{~V}-\mathrm{m}\)

Q.61 The electric flux from a cube of edge \(\ell\) is \(\phi\). What will be its value if edge of cube is made \(2 \ell\) and charge enclosed is halved -

(1) \(\phi / 2\)

(2) \(2 \phi\)

(3) \(4 \phi\)

(4) \(\phi\)

Q.62 A cubical box of side \(1 \mathrm{~m}\) is immersed a uniform electric field of strength \(10^{4} \mathrm{~N} / \mathrm{C}\). The flux through the cube is-

(1) \(10^{4}\)

(2) \(6 \times 10^{4}\)

(3) \(2 \times 10^{4}\)

(4) Zero

Q.63 Figure shows some of the electric field lines corresponding to an electric field. The figure suggests that


(1) \(\mathrm{E}_{\mathrm{A}}>\mathrm{E}_{\mathrm{B}}>\mathrm{E}_{\mathrm{C}}\)

(2) \(\mathrm{E}_{\mathrm{A}}=\mathrm{E}_{\mathrm{B}}=\mathrm{E}_{\mathrm{C}}\)

(3) \(\mathrm{E}_{\mathrm{A}}=\mathrm{E}_{\mathrm{C}}>\mathrm{E}_{\mathrm{B}}\)

(4) \(\mathrm{E}_{\mathrm{A}}=\mathrm{E}_{\mathrm{C}}<\mathrm{E}_{\mathrm{B}}\)

Q.64 A charge of 1 coulomb is located at the centre of a sphere of radius \(10 \mathrm{~cm}\) and a cube of side 20 \(\mathrm{cm}\). The ratio of outgoing flux from the sphere and cube will be :

(1) More than one

(2) Less than one

(3) One

(4) Nothing certain can be said

Q.65 A cylinder of radius \(\mathrm{R}\) and length \(\mathrm{L}\) is placed in a uniform electric field \(\mathrm{E}\) parallel to the cylinder axis. The outward flux over the surface of the cylinder is given by :

(1) \(2 \pi R^{2} E\)

(2) zero

(3) \(2 \pi R L E\)

(4) \(\pi R^{2} E\)

Q.66 A rectangular surface of sides \(10 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) is placed inside a uniform electric field of \(25 \mathrm{~V} /\) \(\mathrm{m}\), such that the surface makes an anagle of \(30^{\circ}\) with the direction of electric field. Find the flux of the electric field throught he rectangular surface :

(1) \(0.1675 \mathrm{~N} / \mathrm{m}^{2} \mathrm{C}\)

(2) \(0.1875 \mathrm{Nm}^{2} / \mathrm{C}\)

(3) Zero

(4) \(0.1075 \mathrm{Nm}^{2} / \mathrm{C}\)

Q.67 A charge \(\mathrm{Q}\) is kept at the corner of a cube. Electric flux passing through one of those faces not touching that charge is :

(1) \(\frac{\mathrm{Q}}{24 \in_{0}}\)

(2) \(\frac{\mathrm{Q}}{3 \in_{0}}\)

(3) \(\frac{\mathrm{Q}}{8 \in_{0}}\)

(4) \(\frac{Q}{6 \epsilon_{0}}\)

Q.68 There is uniform electric field of \(8 \times 10^{3} \hat{\mathrm{i}} \mathrm{N} / \mathrm{C}\). What is the net flux (in SI units) of the uniform electric field through a cube of side \(0.3 \mathrm{~m}\) oriented so that its faces are parallel to the coordinates plane ?

(1) \(2 \times 8 \times 10^{3}\)

(2) \(0.3 \times 8 \times 10^{3}\)

(3) Zero

(4) \(8 \times 10^{6} \times 6\) 

\section{ELECTROSTATICS}

Q.69 If electric lines of force in are represented as shown in the figure, then one can conclude that, electric field is :


(1) Non-uniform

(2) Uniform

(3) Both uniform and non-uniform

(4) Zero everywhere

Q.70 Total flux coming out of some closed surface is :

(1) \(\mathrm{q} / \varepsilon_{0}\)

(2) \(\varepsilon_{0} / \mathrm{q}\)

(3) \(\mathrm{q} \varepsilon_{0}\)

(4) \(\sqrt{q / \varepsilon_{0}}\)

Q.71 Eight charges, \(1 \mu \mathrm{C}, .-7 \mu \mathrm{C},-4 \mu \mathrm{C}, 10 \mu \mathrm{C}, 2 \mu \mathrm{C},-5 \mu \mathrm{C},-3 \mu \mathrm{C}\) and \(6 \mu \mathrm{C}\) are situated at the eight corners of a cube of side \(20 \mathrm{~cm}\). A spherical surface of radius \(80 \mathrm{~cm}\) encloses this cube. The centre of the sphere coincides with the centre of the cube. Then the total outgoing flux from the spherical surface (in unit of volt meter) is-

(1) \(36 \pi \times 10^{3}\)

(2) \(684 \pi \times 10^{3}\)

(3) zero

(4) none of the above

Q.72 Gauss law is given by \(\in_{0} \oint_{\mathrm{s}} \overrightarrow{\mathrm{E}} \cdot \overrightarrow{\mathrm{d} s}=\mathrm{q}\), if net charge enclosed in gaussian surface is zero then :-

(1) E on surface must be zero

(2) incoming and outgoing electric lines are equal

(3) there is a net incoming electric lines

(4) none

Q.73 If the electric flux entering and leaving an closed surface respectively is \(\phi_{1}\) and \(\phi_{2}\) the electric charge inside the surface will be

(1) \(\left(\phi_{1}+\phi_{2}\right) \varepsilon_{0}\)

\((2)\left(\phi_{2}-\phi_{1}\right) \varepsilon_{0}\)

(3) \(\frac{\phi_{1}+\phi_{2}}{\varepsilon_{0}}\)

(4) \(\frac{\phi_{2}-\phi_{1}}{\varepsilon_{0}}\)

Q.74 A nonconducting solid sphere of radius \(\mathrm{R}\) is uniformly charged. The magnitude of the electric field due to the sphere at a distance \(r\) from its centre -

(a) increases as \(r\) increases, for \(r<R\)

(b) decreases as \(\mathrm{r}\) increases, for \(0<\mathrm{r}<\infty\)

(c) decreases as \(\mathrm{r}\) increases, for \(\mathrm{R}<\mathrm{r}<\infty\)

(d) is discontinuous at \(r=R\)

(1) a, c

(2) \(c, d\)

(3) \(a, b\)

(4) b, d

Q.75 A sphere of radius \(\mathrm{R}\) and charge \(\mathrm{Q}\) is placed inside an imaginary sphere of radius \(2 \mathrm{R}\) whose centre coincides with the given sphere. the flux related to imaginary sphere is :-

(1) \(\frac{\mathrm{Q}}{\epsilon_{0}}\)

(2) \(\frac{Q}{2 \in_{0}}\)

(3) \(\frac{4 \mathrm{Q}}{\epsilon_{0}}\)

(4) \(\frac{2 Q}{\epsilon_{0}}\)

Q.76 \(20 \mu \mathrm{C}\) charge is placed inside a closed surface then flux related to surface is \(\phi\). If \(80 \mu \mathrm{C}\) charge is added inside the surface then change in flux is :-

(1) \(4 \phi\)

(2) \(5 \phi\)

(3) \(\phi\)

(4) \(8 \phi\) 

\section{ELECTROSTATICS}

Q.77 A point charge is placed at a distance \(\frac{\mathrm{a}}{2}\) perpendicular to the plane and above the centre of a square of side a. The electric flux through the square is :-

(1) \(\frac{\mathrm{q}}{\epsilon_{0}}\)

(2) \(\frac{\mathrm{q}}{\pi \epsilon_{0}}\)

(3) \(\frac{q}{4 \in_{0}}\)

(4) \(\frac{\mathrm{q}}{6 \in_{0}}\)

\section{ELECTRIC POTENTIAL AND CONDUCTORS}

Q.78 In electric field, a \(6.75 \mu \mathrm{C}\) charge experiences \(2.5 \mathrm{~N}\) force, when placed at distance of \(5 \mathrm{~m}\) from the origin. Then potential gradient at this point will be- (in M.K.S.)

(1) \(5.71 \times 10^{5}\)

(2) \(3.71 \times 10^{5}\)

(3) \(18.81 \times 10^{5}\)

(4) \(1.881 \times 10^{5}\)

Q.79 When charge of 3 coulomb is placed in a uniform electric field, it experiences a force of 3000 newton, within this field, potential difference between two points separated by a distance of \(1 \mathrm{~cm}\) is-

(1) \(10 \mathrm{Volt}\)

(2) 90 Volt

(3) 1000 Volt

(4) 3000 Volt.

Q.80 A uniform electric field having a magnitude \(\mathrm{E}_{0}\) and direction along positive \(\mathrm{x}\)-axis exists.If the electric potential \((\mathrm{V})\) is zero at \(\mathrm{x}=0\), then its value at \(\mathrm{x}=+\mathrm{x}\) will be-

(1) \(\mathrm{V}_{\mathrm{x}}=\mathrm{x} \mathrm{E}_{0}\)

(2) \(\mathrm{V}_{\mathrm{x}}=-\mathrm{x} . \mathrm{E}_{0}\)

(3) \(\mathrm{V}_{\mathrm{x}}=\mathrm{x}^{2} \mathrm{E}_{0}\)

(4) \(V_{x}=x^{2} E_{0}\)

Q.81 The electric potential \(\mathrm{V}\) at any point \((\mathrm{x}, \mathrm{y}, \mathrm{z})\) in space is given by \(\mathrm{V}=4 \mathrm{x}^{2}\) volt. The electric field \(\mathrm{E}\) in \(\mathrm{V} / \mathrm{m}\) at the point \((1,0,2)\) is \(-\)

(1) \(+8\) in \(x\) direction

(2) 8 in \(-\mathrm{x}\) direction

(3) 16 in \(+x\) direction

(4) 16 in \(-x\) direction

Q.82 Charges of \(+\left(\frac{10}{3}\right) \times 10^{-9}\) are placed at each of the four corners of a square of side \(8 \mathrm{~cm}\). The potential at the intersection of the diagonals is

(1) \(150 \sqrt{2}\) Volt

(2) \(1500 \sqrt{2}\) Volt

(3) \(900 \sqrt{2}\) Volt

(4) 900 Volt

Q.83 The electric potential (V) as a function of distance (x) [in meters] is given by \(\mathrm{V}=\left(5 \mathrm{x}^{2}+10 \mathrm{x}-9\right)\) Volt. The value of electric field at \(\mathrm{x}=1 \mathrm{~m}\) would be-

(1) \(20 \mathrm{Volt} / \mathrm{m}\) (2) \(6 \mathrm{Volt} / \mathrm{m}\)

(3) \(11 \mathrm{Volt} / \mathrm{m}\)

(4) \(-23 \mathrm{Volt} / \mathrm{m}\)

Q.84 A positive point charge \(\mathrm{q}\) is carried from a point \(\mathrm{B}\) to a point \(\mathrm{A}\) in the electric field of a point charge \(+\mathrm{Q}\) at \(\mathrm{O}\). If the permittivity of free space is \(\varepsilon_{0}\), the work done in the process is given by \((\) where \(\mathrm{a}=\mathrm{OA}\) and \(\mathrm{b}=\mathrm{OB})\) -

(1) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a}+\frac{1}{b}\right)\)

(2) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a}-\frac{1}{b}\right)\)

(3) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a^{2}}-\frac{1}{b^{2}}\right)\)

(4) \(\frac{q Q}{4 \pi \varepsilon_{0}}\left(\frac{1}{a^{2}}+\frac{1}{b^{2}}\right)\) 

\section{ELECTROSTATICS}

Q.85 Some equipotential lines are as shown is fig. \(E_{1}, E_{2}\) and \(E_{3}\) are the electric fields at points 1,2 and 3 then -

(1) \(\mathrm{E}_{1}=\mathrm{E}_{2}=\mathrm{E}_{3}\)

(2) \(\mathrm{E}_{1}>\mathrm{E}_{2}>\mathrm{E}_{3}\)

(3) \(\mathrm{E}_{1}>\mathrm{E}_{2}, \mathrm{E}_{2}<\mathrm{E}_{3}\)

(4) \(\mathrm{E}_{1}<\mathrm{E}_{2}<\mathrm{E}_{3}\)


Q.86 A \(\alpha\)-particle moves towards a rest nucleus, if kinetic energy of \(\alpha\)-particle is \(10 \mathrm{MeV}\) and atomic number of nucleus is 50 . The closest approach will be -

(1) \(1.44 \times 10^{-14} \mathrm{~m}\)

(2) \(2.88 \times 10^{-14} \mathrm{~m}\)

(3) \(1.44 \times 10^{-10} \mathrm{~m}\)

(4) \(2.88 \times 10^{-10} \mathrm{~m}\)

Q.87 \(A, B, C\) and \(D\) are four points on an imaginary circle in region containing uniform electric field as shown in figure. Select the incorrect option

(1) \(V_{B}>V_{A}\)

(2) \(V_{B}>V_{C}\)

(3) \(V_{B}<V_{D}\)

(4) \(V_{A}>V_{D}\)


Q.88 When a negative charge is released and moves in electric field, it moves toward a position of

(1) lower electric potential and lower potential energy

(2) lower electric potential and higher potential energy

(3) higher electric potential and lower potential energy

(4) higher electric potential and higher potential energy

Q.89 Four equal charges of charge \(q\) are placed at corner of a square of side a. Potential energy of the whole system is-

(1) \(\frac{4 \mathrm{kq}^{2}}{\mathrm{a}}\)

(2) \(\frac{4 \mathrm{kq}^{2}}{\mathrm{a}}\left(1+\frac{1}{2 \sqrt{2}}\right)\)

(3) \(\frac{1}{2 \sqrt{2}} \frac{k q^{2}}{a}\)

(4) \(\frac{k q^{2}}{a}\left(4+\frac{1}{2 \sqrt{2}}\right)\)

Q.90 Two points \(\mathrm{P}\) and \(\mathrm{Q}\) are maintained at the potentials of \(10 \mathrm{~V}\) and \(-4 \mathrm{~V}\), respectively. The work done in moving 100 electrons from \(\mathrm{P}\) to \(\mathrm{Q}\) is -

(1) \(-9.60 \times 10^{-17} \mathrm{~J}\)

(2) \(9.60 \times 10^{-17} \mathrm{~J}\)

(3) \(-2.24 \times 10^{-16} \mathrm{~J}\)

(4) \(2.24 \times 10^{-16} \mathrm{~J}\)

Q.91 The work done required to put the four charges together at the corners of a square of side a, as shown in the figure is :


(1) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{q^{2}}{a}\)

(2) \(-\frac{2.6}{4 \pi \varepsilon_{0}} \frac{q^{2}}{a}\)

(3) \(+\frac{2.6}{4 \pi \varepsilon_{0}} \frac{q^{2}}{a}\)

(4) None of these Q.92 Three charges \(-\mathrm{q},+\mathrm{Q}\) and \(-\mathrm{q}\) are placed in a straight line as shown.


If the total potential energy of the system is zero, then the ratio \(\frac{\mathrm{q}}{\mathrm{Q}}\) is

(1) 2

(2) \(5.5\)

(3) 4

(4) \(1.5\)

Q.93 Electric field at a distance \(\mathrm{x}\) from origin is given as \(\mathrm{E}=\frac{100}{\mathrm{x}^{2}}\), then potential between points situated at \(\mathrm{x}=10 \mathrm{~m}\) and \(\mathrm{x}=20 \mathrm{~m}\).

(1) \(5 \mathrm{~V}\)

(2) \(10 \mathrm{~V}\)

(3) \(15 \mathrm{~V}\)

(4) \(4 \mathrm{~V}\)

Q.94 Figure shows a set of equipotential surfaces. The magnitude and direction of electric field that exists in the region is-

(1) \(10 \sqrt{2} \mathrm{~V} / \mathrm{m}\) at \(45^{\circ}\) with \(\mathrm{x}\)-axis

(2) \(10 \sqrt{2} \mathrm{~V} / \mathrm{m}\) at \(-45^{\circ}\) with \(x\)-axis

(3) \(5 \sqrt{2} \mathrm{~V} / \mathrm{m}\) at \(45^{\circ}\) with \(\mathrm{x}\)-axis

(4) \(5 \sqrt{2} \mathrm{~V} / \mathrm{m}\) at \(-45^{\circ}\) with \(\mathrm{x}\)-axis


Q.95 The variation of potential with distance \(\mathrm{R}\) from a fixed point is as shown in the figure. The electric field at \(\mathrm{R}=5 \mathrm{~m}\) is :

(1) \(2.5 \mathrm{~V} / \mathrm{m}\)

\((2)-2.5 \mathrm{~V} / \mathrm{m}\)

(3) \((2 / 5) \mathrm{V} / \mathrm{m}\)

\((4)-(2 / 5) \mathrm{V} / \mathrm{m}\)


Q.96 A hollow conducting sphere of radius \(\mathrm{R}\) has charge \((+\mathrm{Q})\) on its surface. The electric potential within the sphere at a distance \(r=\frac{R}{3}\) from the centre is -

(1) Zero

(2) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r}\)

(3) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{R}\)

(4) \(\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{r^{2}}\)

Q.97 A large isolated metal sphere of radius (R) carries a fixed charge. A small charge is placed at a distance (r) from its surface experiences a force which is -

(1) Proportional to \(\mathrm{R}\)

(2) Independent of \(\mathrm{R}\) and

(3) Inversely proportional to \((\mathrm{R}+\mathrm{r})^{2}\)

(4) inversely proportional to \(r^{2}\)

Q.98 A uniform hollow sphere of charge does not produce an electric field at any-

(1) Interior point

(2) Outer point

(3) Surface point

(4) None of the above Q.99 Which of the following graphs show how the electric field strength \(E\) varies with distance \(r\) from the centre of the some conducting sphere ?


Q.100 The electric field intensity at \(\mathrm{P}\) and \(\mathrm{Q}\), in the shown arrangement, are in the ratio :


(1) \(1: 2\)

(2) \(2: 1\)

(3) \(1: 1\)

(4) \(4: 1\)

Q.101 Two isolated metallic spheres of radii \(2 \mathrm{~cm}\) and \(4 \mathrm{~cm}\) are given equal charge, then the ratio of charge density on the surfaces of the spheres will be ?:

(1) \(1: 2\)

(2) \(4: 1\)

(3) \(8: 1\)

(4) \(1: 4\)

Q.102 Two concentric hollow conducting spheres of radius \(\mathrm{r}\) and \(\mathrm{R}\) are shown. The charge on outer shell is \(\mathrm{Q}\). What charge should be given to inner sphere so that the potential at any point \(\mathrm{P}\) outside the outer sphere is zero?


(1) \(-\frac{\mathrm{Qr}}{\mathrm{R}}\)

(2) \(-\frac{\mathrm{QR}}{\mathrm{r}}\)

(3) \(-\mathrm{Q}\)

(4) \(-\frac{2 \mathrm{QR}}{\mathrm{r}}\)

\section{ELECTRIC DIPOLE}

Q.103 An electric dipole with dipole moment \(\vec{P}=(2 \hat{i}+3 \hat{j}) \mathrm{cm}\) is kept in electric field \(\vec{E}=4 \hat{i} \mathrm{~N} / \mathrm{C}\). The torque acting on it is

(1) \(-12 \hat{k}(\mathrm{Nm})\)

(2) \(8 \hat{k}\)

(3) \(12 \hat{k}(\mathrm{Nm})\)

(4) \(-8 \hat{k}\)

Q.104 An electric dipole when placed in a uniform electric field \(\vec{E}\) will have maximum potential energy if the dipole moment makes the following angle with \(\vec{E}\)

(1) \(\pi\)

(2) \(\frac{3 \pi}{2}\)

(3) Zero

(4) \(\frac{\pi}{2}\) 

\section{ELECTROSTATICS}

Q.105 An electric dipole has the magnitude of its charge as \(\mathrm{q}\) and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively

(1) 2 q.E and minimum

(3) Zero and minimum

(2) q.E and p.E

(4) Zero and maximum

Q.106 An electric dipole is placed in non-uniform electric field. It may experience :

(1) Resultant force and couple

(2) Only resultant force

(3) Only couple

(4) All of these

Q.107 An electron released on the axis of a positively charged ring at a large distance from the centre will :

(1) Not move

(2) Do oscillatory motion

(3) Do SHM

(4) Do non periodic motion

Q.108 Two charges of \(+25 \times 10^{-9}\) coulomb and \(-25 \times 10^{-9}\) coulomb are placed \(6 \mathrm{~m}\) apart. Find the electric field intensity ratio at points \(4 \mathrm{~m}\) from the centre of the electric dipole (i) on axial line (ii) on equatorial line:

(1) \(\frac{1000}{49}\)

(2) \(\frac{49}{1000}\)

(3) \(\frac{500}{49}\)

(4) \(\frac{49}{500}\)

Q.109 The electric force on a point charge situated on the axis of a short dipole is \(F\). If the charge is shifted along the axis to do+uble the distance, the electric force acting will be :

(1) \(4 \mathrm{~F}\)

(2) \(\frac{F}{2}\)

(3) \(\frac{\mathrm{F}}{4}\)

(4) \(\frac{\mathrm{F}}{8}\)

Q.110 An electric dipole when placed in a uniform electric field E will have minimum potential energy, when the angle made by dipole moment with field \(\mathrm{E}\) is :

(1) \(\pi\)

(2) \(\frac{3 \pi}{2}\)

(3) Zero

(4) \(\frac{\pi}{2}\)

Q.111 The electric potential in volts due to an electric dipole of dipole moment \(2 \times 10^{-8}\) coulomb-metre at a distance of \(3 \mathrm{~m}\) on a line making an angle of \(60^{\circ}\) with the axis of the dipole is :

(1) 0

(2) 10

(3) 20

(4) 40

Q.112 An electric dipole of length \(2 \mathrm{~cm}\) is placed with its axis making an angle of \(30^{\circ}\) to a uniform electric field \(10^{5} \mathrm{~N} / \mathrm{C}\). If it experiences a torque of \(10 \sqrt{3} \mathrm{Nm}\), then potential energy of the dipole

\((1)-10 \mathrm{~J}\)

\((2)-20 \mathrm{~J}\)

\((3)-30 \mathrm{~J}\)

\((4)-40 \mathrm{~J}\)

Q.113 If an electric dipole is kept in a non-uniform electric field, then it will experience -

(1) only torque

(2) no torque

(3) a resultant force and a torque

(4) only a force 

\section{ELECTROSTATICS}

Q.114 A dipole of dipole moment \(p\), is placed in an electric field \(\vec{E}\) and is in stable equilibrium. The torque required to rotate the dipole from this position by angle \(\theta\) will be -

(1) \(\mathrm{pE} \cos \theta\)

(2) \(\mathrm{pE} \sin \theta\)

(3) \(\mathrm{pE} \tan \theta\)

(4) \(-\mathrm{pE} \cos \theta\)

Q.115 The electric potential at a point due to an electric dipole will be -

(1) \(\frac{k(\vec{p} \cdot \vec{r})}{r^{3}}\)

(2) \(\frac{k(\vec{p} \cdot \vec{r})}{r^{2}}\)

(3) \(\frac{k(\vec{p} \times \vec{r})}{r}\)

(4) \(\frac{k(\vec{p} \times \vec{r})}{r^{2}}\)

Q.116 An electric dipole is made up of two equal and opposite charges of \(2 \times 10^{-6}\) coulomb at a distance of \(3 \mathrm{~cm}\). This is kept in an electric field of \(2 \times 10^{5} \mathrm{~N} / \mathrm{C}\), then the maximum torque acting on the dipole -

(1) \(12 \times 10^{-1} \mathrm{Nm}\)

(2) \(12 \times 10^{-3} \mathrm{Nm}\)

(3) \(24 \times 10^{-3} \mathrm{Nm}\)

(4) \(24 \times 10^{-1} \mathrm{Nm}\)

Q.117 The electric potential in volt at a distance of \(0.01 \mathrm{~m}\) on the equatorial line of an electric dipole of dipole moment \(p\) is -

(1) \(p / 4 \pi \epsilon_{0} \times 10^{-4}\)

(2) zero

(3) \(4 \pi \epsilon_{0} p \times 10^{-4}\)

(4) \(4 \pi \in_{0} / p \times 10^{-4}\)

Q.118 When an electric dipole \(\overrightarrow{\mathrm{p}}\) is kept in a uniform electric field \(\overrightarrow{\mathrm{E}}\) then for what value of the angle between \(\overrightarrow{\mathrm{p}}\) and \(\overrightarrow{\mathrm{E}}\), torque will be maximum :-

(1) \(90^{\circ}\)

(2) \(0^{\circ}\)

(3) \(180^{\circ}\)

(4) \(45^{\circ}\)

Q.119 What will be the ratio of electric field at the axis and at equatorial line of a dipole :-

(1) \(1: 2\)

(2) \(2: 1\)

(3) \(4: 1\)

(4) \(1: 4\)

Q.120 For a dipole \(q=2 \times 10^{-6} \mathrm{C} ; \mathrm{d}=0.01 \mathrm{~m}\) find the maximum torque on the dipole if \(\mathrm{E}=5 \times 10^{5} \mathrm{~N} / \mathrm{C}:-\)

(1) \(1 \times 10^{-3} \mathrm{Nm}^{-1}\)

(2) \(10 \times 10^{-3} \mathrm{Nm}^{-1}\)

(3) \(10 \times 10^{-3} \mathrm{Nm}\)

(4) \(1 \times 10^{2} \mathrm{Nm}^{2}\)

Q.121 In an electric field electric dipole is rotated though an angle \(\theta\), then work done will be

(1) \(\mathrm{pE}(1-\cos \theta)\)

(2) \(\mathrm{pE} \sin \theta\)

(3) zero

(4) \(-\mathrm{pE} \cos \theta\)