PHYSICS FOR JEE

1. Two equal charges as separated by distanced. A third charge placed on a perpendicular bisector at \(x\) distance from centre will experience maximum coulomb force, when

a) \(x=d / \sqrt{2}\)

b) \(x=d / 2\)

c) \(x=d / 2 \sqrt{2}\)

d) \(x=d / 2 \sqrt{3}\)

2. Two large metal plates are placed parallel to each other. The inner surfaces of plates are charged by \(+\sigma\) and \(-\sigma\left(\mathrm{cm}^{-2}\right)\). The outer surfaces are neutral. The electric field in the region between the plates and outside the plates is

a) \(\frac{2 \sigma}{\varepsilon_{0}}, \frac{\sigma}{\varepsilon_{0}}\)

b) \(\frac{\sigma}{\varepsilon_{0}}\), zero

c) \(\frac{2 \sigma}{\varepsilon_{0}}, \operatorname{zero}\)

d) \(\operatorname{zero}, \frac{2 \sigma}{\varepsilon_{0}}\)

3. A point \(Q\) lies on the perpendicular bisector of an electrical dipole of dipole moment \(p\). If the distance of \(Q\) from the dipole is \(r\) (much larger than the size of the dipole), then the electric intensity \(E\) at \(Q\) is proportional to

a) \(r^{-2}\)

b) \(r^{-4}\)

c) \(r^{-1}\)

d) \(r^{-3}\)

4. The distance between two point charges has increased by \(10 \%\). The force of interaction between them

a) Increased by \(10 \%\)

b) decreased by \(10 \%\)

c) decreased by \(17 \%\)

d) decreased by \(21 \%\)

5. The potential of the electric field produced by point charge at any point \((x, y, z)\) is given by \(V=3 x^{2}+5\), where \(x, y\) are in metres and \(V\) is in volts. The intensity of the electric field at \((-2,1,0)\) is

a) \(+17 \mathrm{Vm}^{-1}\)

b) \(-17 \mathrm{Vm}^{-1}\)

c) \(+12 \mathrm{Vm}^{-1}\)

d) \(-12 \mathrm{Vm}^{-1}\)

6. Three charges \(-q_{1}+q_{2}\) and \(-q_{3}\) are placed as shown in figure. The \(x\) component of the force on \(-q_{1}\) is proportional to

a) \(\frac{q_{2}}{b^{2}}-\frac{q_{3}}{b^{2}} \sin \theta\)

b) \(\frac{q_{2}}{b^{2}}-\frac{q_{3}}{b^{2}} \cos \theta\)

c) \(\frac{q_{2}}{b^{2}}+\frac{q_{3}}{b^{2}} \sin \theta\)

d) \(\frac{q_{2}}{b^{2}}+\frac{q_{3}}{b^{2}} \cos \theta\)

7. Four metal conductors having different shapes

I. A sphere II. Cylinder

III. Pear

IV. Lightning conductor

are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time is

a) 1

b) 2

c) 3

d) 4

8. The electric intensity outside a charged sphere of radius \(R\) at a distance \(r(r>R)\) is

a) \(\frac{\sigma R^{2}}{\varepsilon_{0} r^{2}}\)

b) \(\frac{\sigma r^{2}}{\varepsilon_{0} R^{2}}\)

c) \(\frac{\sigma r}{\varepsilon_{0} R}\)

d) \(\frac{\sigma R}{\varepsilon_{0} r}\)

9. Two identical positive charges are fixed on the \(y\)-axis at equal distances from the origin \(O\). A negatively charged particle starts on the \(x\)-axis, at a large distance from \(O\), moves along the \(x\)-axis, passes through \(O\) and moves far away from \(O\). Its acceleration \(a\) is taken as positive along its direction of motion. The best graph between the particle's acceleration and its \(x\)-coordinate is represented by

10. A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

a) A potential difference appears between the two cylinders when a charge density is given to the inner cylinder

b) A potential difference appears between the two cylinders when a charge density is given to the outer cylinder

c) No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders

d) No potential difference appears between the two cylinders when same charge density is given to both the cylinders

11. A wooden block performs SHM on a frictionless surface with frequency \(v_{0}\). The block carries a charge \(+Q\) on its surface. If now a uniform electric field \(\mathbf{E}\) is switched on as shown, then the SHM of the block will be

a) of the same frequency and with shifted mean position

b) of the same frequency and with same mean position

c) of changed frequency and with shifted mean position

d) of changed frequency and with same mean position

12. Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

a) negative and distributed uniformly over the surface of the sphere

b) negative and appears only at the point on the sphere closest to the point charge 

c) Negative and distributed non-uniformly over the entire surface of the sphere

d) Zero

13. A infinite number of charges, each of charge \(1 \mu \mathrm{C}\), are placed on the \(x\)-axis with co-ordinates \(x=1,2,4,8\), \(\ldots \infty\). If a charge of \(1 \mathrm{C}\) is kept at the origin, then what is the net force acting on \(1 \mathrm{C}\) charge?

a) \(9000 \mathrm{~N}\)

b) \(12000 \mathrm{~N}\)

c) \(24000 \mathrm{~N}\)

d) \(36000 \mathrm{~N}\)

14. The electric field due to an electric dipole at a distance \(r\) from its centre in axial position is \(E\). If the dipole is rotated through an angle of \(90^{\circ}\) about its perpendicular axis, the electric field at the same point will be

a) \(\mathrm{E}\)

b) \(\frac{E}{4}\)

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

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

15. A charge \(Q\).is divided in two parts \(Q-q\).What is value of \(q\) for maximum force between them?

a) \(\frac{3 Q}{4}\)

b) \(\frac{Q}{3}\)

c) \(Q\)

d) \(\frac{Q}{2}\)

16. Under the influence of the coulomb field of charge+ \(Q\), a charge \(-q\) is moving around it in an elliptical orbit .Find out the correct statements(s).

a) The angular momentum of the charge \(-q\) is constant

b) The linear momentum of the charge \(-q\) is constant

c) The angular velocity of the charge \(-q\) is constant

d) The linear speed of the charge \(-q\) is constant

17. Infinite charges of magnitude \(q\) each are lying at \(x=1,2,4,8\)..metre on \(X\)-axis. The value of intensity of electric field at point \(x=0\) due to these charges will be

a) \(12 \times 10^{9} q N C^{-1}\)

b) zero

c) \(6 \times 10^{9} q N C^{-1}\)

d) \(4 \times 10^{9} q N C^{-1}\)

18. A hollow metallic sphere of radius \(10 \mathrm{~cm}\) is given a charge of \(3.2 \times 10^{-9}\) C. The electric intensity at a point 4 \(\mathrm{cm}\) from the centre is

a) \(9 \times 10^{-9} \mathrm{NC}^{-1}\)

b) \(288 \mathrm{NC}^{-1}\)

c) \(2.88 \mathrm{NC}^{-1}\)

d) Zero

19. Dimensions of \(\varepsilon_{0}\) are

a) \(M^{-1} L^{-3} T^{4} A^{2}\)

b) \(M^{0} L^{-3} T^{3} A^{3}\)

c) \(M^{-1} L^{-3} T^{3} A\)

d) \(M^{-1} L^{-3} T A^{2}\)

20. What about Gauss theorem is not incorrect?

a) It can be derived by using Coulomb's law

b) It is valid for conservative field, obeys inverse square root law

c) Gauss theorem is not applicable in gravitation

d) Both (a) and (b)

21. Two identical charges repel each other with a force equal to \(10 \mathrm{mg}\) wt when they are \(0.6 \mathrm{~m}\) apart in air ( \(g=10 \mathrm{~ms}^{-2}\) ). The value of each charge is

a) \(2 \mathrm{mC}\)

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

c) \(2 \mathrm{nC}\)

d) \(2 \mu \mathrm{C}\)

22. The spatial distribution of the electric field due to charges \((A, B)\) is shown in figure. Which one of the following statements is correct? 

a) \(A\) is + ve and \(B-v e,|A|>|B|\)

b) \(A\) is - ve and \(B+v e,|A|=|B|\)

c) Both are +ve but \(A>B\)

d) Both are-ve but \(A>B\)

23. A conductor having a cavity is given a positive charge. Then field strengths \(E_{A^{\prime}} E_{B}\) and \(E_{C}\) at point \(A\) (within cavity), at \(B\) (within conductor but outside cavity) and \(C\) (near conductor) respectively will be

a) \(E_{A}=0, E_{B}=0, E_{c}=0\)

b) \(E_{A}=0, E_{B}=0, E_{c} \neq 0\)

c) \(E_{A} \neq 0, E_{B}=0, E_{C} \neq 0\)

d) \(E_{A} \neq 0, E_{B} \neq 0, E_{C} \neq 0\)

24. The electric field at the centroid of an equilateral triangle carrying an equal charge \(q\) at each of the vertices is

a) Zero

b) \(\frac{\sqrt{2 k q}}{r^{2}}\)

c) \(\frac{k q}{\sqrt{2 r^{2}}}\)

d) \(\frac{3 k q}{r^{2}}\)

25. An electric dipole has a pair of equal and opposite point charges \(q\) and \(-q\) separated by a distance \(2 x\). The axis of the dipole is defined as

a) Direction from positive charge to negative charge

b) Direction from negative charge to positive charge

c) Perpendicular to the line joining the two charges drawn at the centre and pointing upward direction

d) Perpendicular to the line joining the two charges drawn at the centre and pointing downward direction

26. Two small conducting sphere of equal radius have charges \(+10 \mu \mathrm{C}\) and \(-20 \mu \mathrm{C}\) respectively and placed at a distance \(R\) from each other experience force \(F_{1}\). If they are brought in contact and separated to the same distance, they experience force \(F_{2}\). the ratio of \(F_{1}\) to \(F_{2}\) is

a) \(1: 2\)

b) \(-8: 1\)

c) \(1: 8\)

d) \(-2: 1\)

27. Two long conductors, separated by a distance \(d\) carry currents \(I_{1}\) and \(I_{2}\) in the same direction. They exert a force \(F\) on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to \(3 d\). The new value of the force between them is

a) \(-2 F\)

b) \(F / 3\)

c) \(-2 F / 3\)

d) \(-F / 3\)

28. Charge \(q_{1}=+6.0 \mathrm{nC}\) is on \(Y\) - axis at \(\mathrm{y}=+3 \mathrm{~cm}\) and charge \(q_{2}=-6.0 \mathrm{nC}\) is on \(Y\) - axis at \(\mathrm{y}=-3 \mathrm{~cm}\) calculate force on a test charge \(q_{0}=2 \mathrm{nC}\) placed on \(X\)-axis at \(x=4 \mathrm{~cm}\).

a) \(-51.8 \hat{j} \mu \mathrm{N}\)

b) \(+51.8 \hat{j} \mu \mathrm{N}\)

c) \(-5.18 \hat{j} \mu \mathrm{N}\)

d) \(5.18 \hat{j} \mu \mathrm{N}\)

29. The electric flux for Gaussian surface \(A\) that enclose the charged particles in free space is \(\left(\right.\) given \(\left.q_{1}=-14 n C, q_{2}=78.85 n C, q_{3}=-56 n C\right)\)

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

b) \(10^{3} \mathrm{CN}^{-1} \mathrm{~m}^{-2}\)

c) \(6.32 \times 10^{3} \mathrm{Nm}^{2} \mathrm{C}^{-1}\)

d) \(6.32 \times 10^{3} \mathrm{CN}^{-1} \mathrm{~m}^{-1}\)

30. A metallic spherical shell of radius \(R\) has a charge \(-Q\) on it. A point charge \(+Q\) is placed at the centre of the shell. Which of the graphs shown below may correctly represent the variation of the electric field \(E\) with distance \(r\) from the centre of the shell?

31. A charge \(q\) is placed at the corner of a cube of sidea. The electric flux through the cube is

a) \(\frac{q}{\varepsilon_{0}}\)

b) \(\frac{q}{3 \varepsilon_{0}}\)

c) \(\frac{q}{6 \varepsilon_{0}}\)

d) \(\frac{q}{8 \varepsilon_{0}}\)

32. If the electric flux entering and leaving an enclosed surface respectively are \(\phi_{1}\) and \(\phi_{2}\), the electric charge inside the surface will be

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

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

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

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

33. Which of the following statement is correct?

a) Electric field is zero on the surface of current carrying wire.

b) Electric field is non-zero on the axis of hollow current carrying wire

c) Surface integral of magnetic field for any closed surface is equal to \(\mu_{0}\) times of total algebraic sum of current which are crossing through the closed surface

d) None of the above

34. The ratio of electric fields on the axis and at equator of an electric dipole will be

a) \(1: 1\)

b) \(2: 1\)

c) \(4: 1\)

d) \(1: 4\)

35. A neutral water molecule \(\left(\mathrm{H}_{2} \mathrm{O}\right)\) in its vapour state has an electric dipole moment of \(6 \times 10^{-30} \mathrm{Cm}\). If the molecule is placed in an electric field of \(1.5 \times 10^{4} \mathrm{NC}^{-1}\), the maximum torque that the field can exert on it is nearly

a) \(4.5 \times 10^{-26} \mathrm{~N}-\mathrm{m}\)

b) \(4 \times 10^{-34} \mathrm{~N}-\mathrm{m}\)

c) \(9 \times 10^{-26} \mathrm{~N}-\mathrm{m}\)

d) \(6 \times 10^{-26} \mathrm{~N}-\mathrm{m}\)

36. An electric dipole is placed at an angle of \(60^{\circ}\) with an electric field of intensity \(10^{5} \mathrm{NC}^{-1}\). It experiences a torque equal to \(8 \sqrt{3} \mathrm{Nm}\). Calculate the charge on the dipole, if the dipole length is \(2 \mathrm{~cm}\).

a) \(-8 \times 10^{3} \mathrm{C}\)

b) \(8.54 \times 10^{-4} \mathrm{C}\)

c) \(8 \times 10^{-3} \mathrm{C}\)

d) \(0.85 \times 10^{-6} \mathrm{C}\)

37. Two identical conducting balls \(A\) and \(B\) have positive charges \(q_{1}\) and \(q_{2}\) respectively but \(q_{1} \neq q_{2}\). The balls are brought together so that they touch each other and then kept in their original positions. The force between them is

a) Less than that before the balls touched

b) Greater than that before the balls touched

c) Same as that before the balls touched

d) Zero 38. The charge \(q\) is projected into a uniform electric field \(E\), work done when it moves a distance \(Y\) is

a) \(q E Y\)

b) \(\frac{q Y}{E}\)

c) \(\frac{q E}{Y}\)

d) \(\frac{Y}{q E}\)

39. The Gaussian surface for calculating the electric field due to a charge distribution is 

a) Any surface near the charge distribution

b) Always a spherical surface

c) A symmetrical closed surface containing the charge distribution, at every point of which electric field has a single fixed value

d) None of the given options

40. Three infinitely charged sheets are kept parallel to \(x-y\) plane having charge densities as shown in figure. Then the value of electric field at point \(P\) is

a) \(-\frac{2 \sigma}{\varepsilon_{0}} \hat{k}\)

b) \(\frac{2 \sigma}{\varepsilon_{0}} \hat{k}\)

c) \(-\frac{4 \sigma}{\varepsilon_{0}} \hat{k}\)

d) \(\frac{4 \sigma}{\varepsilon_{0}} \hat{k}\)

41. Two spherical conductors \(A\) and B of radii \(1 \mathrm{~mm}\) and \(2 \mathrm{~mm}\) are separated by a distance of \(5 \mathrm{~cm}\) and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres \(A\) and \(B\) is

a) \(4: 1\)

b) \(1 ; 2\)

c) \(2: 1\)

d) \(1: 4\)

42. Potential and field strength at a certain distance from a point charge are \(600 \mathrm{~V}\) and \(200 \mathrm{NC}^{-1}\). Distance of the point from the charge is

a) \(2 \mathrm{~m}\)

b) \(4 \mathrm{~m}\)

c) \(8 \mathrm{~m}\)

d) \(3 m\)

43. A molecule with a dipole moment \(p\) is placed in an electric field of strength \(E\). Initially the dipole is aligned parallel to the field. If the dipole is to be related to be anti-parallel to the field the work required to be done by an external agency is

a) \(-2 p E\)

b) \(-p E\)

c) \(p E\)

d) \(2 p E\)

44. Two identical metal spheres charged with \(+12 \mu \mathrm{F}\) and \(-8 \mu \mathrm{F}\) are kept at certain distance in air. They are brought into contact and then kept at the same distance. The ratio of the magnitudes of electrostatic forces between them before them and after contact is

a) 12:1

b) \(8: 1\)

c) \(24: 1\)

d) \(4: 1\)

45. Three infinitely long charge sheets are placed as shown in figure. The electric field at point \(P\) is

a) \(\frac{2 \sigma}{\varepsilon_{0}} \hat{k}\)

b) \(-\frac{2 \sigma}{\varepsilon_{0}} \hat{k}\)

c) \(\frac{4 \sigma}{\varepsilon_{0}} \hat{k}\)

d) \(-\frac{4 \sigma}{\varepsilon_{0}} \hat{k}\)

46. The ratio of electric field and potential \((E / V)\) at mid-point of electric dipole, for which separation lis 

a) \(1 / l\)

b) \(l\)

c) \(2 / l\)

d) None of these

47. The figure shows four situations in which charges as indicated \((q>0)\) are fixed on an axis .In which situation is there a point to the left of the charges where an electron would be in equilibrium?

a) 1 and 2

b) 2 and 4

c) 3 and 4

d) 1 and 3

48. If charge \(q\) is placed at the centre of the line joining two equal charges \(Q\), the system of these charges will be the same distance would be

a) \(-4 Q\)

b) \(-Q / 4\)

c) \(-Q / 2\)

d) \(+Q / 2\)

49. Charges \(+2 \mathrm{q},+\mathrm{q}\) and \(+\mathrm{q}\) are placed at the corners \(A, B\) and \(C\) of an equilateral triangle \(A B C\). If \(\mathrm{E}\) is the electric field at the circumcentre 0 of the triangle, due to the charge \(+\mathrm{q}\), then the magnitude and direction of the resultant electric field at 0 is

a) \(E\) along \(A O\)

b) \(2 E\) along \(A O\)

c) \(E\) along \(B O\)

d) \(E\) along \(C O\)

50. The electric field at a point due to an electric dipole, on an axis inclined at an angle \(\theta\left(<90^{\circ}\right)\) to the dipole axis, is perpendicular to the dipole axis, if the angle \(\theta\) is

a) \(\left(\frac{1}{\sqrt{2}}\right)\)

b) \((\sqrt{2})\)

c) \(\left(\frac{1}{2}\right)\)

d) (2)