1. A metal cube of side 5 cm is charged with 6μC. The surface charge density on the cube is

(1).0.125 × 10⁻³Cm⁻²

(2). 0.25 × 10⁻³Cm⁻²

(3). 4 × 10⁻³Cm⁻²

(4). 0.4 × 10⁻³Cm⁻²

2. The value of electric potential at a distance of 9 cm from the point charge 4 × 10⁻⁷C is (Take \( \frac{1}{4πϵ_0} = 9 × 10^9 \) Nm²C^-2)

(1).4 × 10² V

(2). 44.4 V

(3). 4.4 × 10⁵ V

(4). 4 × 10⁴ V

3. A 12pF capacitor is connected to a 50 V battery, the electrostatic energy stored in the capacitor in nJ is

(1).15

(2). 7.5

(3). 0.3

(4). 150

4. The capacitance of a capacitor with charge q and a potential difference V depends on

(1).both q and V

(2). the geometry of the capacitor

(3). q only

(4). V only

5. The steady state current in the circuit shown below is

(1).0.67 A

(2). 1.5 A

(3). 2 A

(4). 1 A

6. A thin spherical shell is charged by some source. The potential difference between the two points C and P (in V ) shown in the figure is: (Take \( \frac{1}{4πϵ0} = 9 × 10^9 \) SI units)

(1).3 × 10⁵

(2). 1 × 10⁵

(3). 0.5 × 10⁵

(4). Zero

7. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .Assertion A: The potential (V) at any axial point, at 2m distance (r) from the centre of the dipole of dipole moment vector \(\vec{P}\) of magnitude, 4 ×10⁻⁶Cm , is ± 9 × 10³V. (Take \(\frac{1}{4πϵ_0} = 9 × 10^9\) SI units). Reason R: V = ± \(\frac{2P}{4πϵ_0r^2}\) where r is the distance of any axial point, situated at 2m from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

(1).Both A and R are true and R is the correct explanation of A.

(2). Both A and R are true and R is NOT the correct explanation of A.

(3). A is true but R is false.

(4). A is false but R is true.

8. In the following circuit, the equivalent capacitance betweenterminal A and terminal B is :

(1).2µF

(2). 1µF

(3). 0.5µF

(4). 4µF

9. If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then A. the charge stored in it, increases. B. the energy stored in it, decreases. C. its capacitance increases. D. the ratio of charge to its potential remains the same. E. the product of charge and voltage increases. Choose the most appropriate answer from the options given below:

(1).A, B and E only

(2). A, C and E only

(3). B, D and E only

(4). A, B and C only

10. A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates:

(1).There is no current

(2). Displacement current of magnitude equal to I flows in the same direction as I

(3). Displacement current of magnitude equal to I flows in a direction opposite to that of I

(4). Displacement current of magnitude greater than I flows but can be in any direction

11.

(1).The magnitude of electric field on the surface is constant

(2). All the charges must necessarily be inside the surface

(3). The electric field inside the surface is necessarily uniform

(4). The number of flux lines entering the surface must be equal to the number of flux lines leaving it

12. An electric dipole is placed at an angle of \(30^\circ\) with an electric field of intensity \(2 × 10^5NC^{−1}\). It experiences a torque equal to 4 Nm. Calculate the magnitude of charge on the dipole, if the dipole length is 2cm.

(1).6 mC

(2). 4 mC

(3). 2 mC

(4). 8 mC

13. The equivalent capacitance of the system shown in the following circuitis

(1).3 µF

(2). 6 µF

(3). 9 µF

(4). 2 µF

14. An electric dipole is placed as shown in the figure.

The electric potential in \(10^2\,V\) at point P due to the dipole is (\(E_0 =\).permittivity of free space and \(\frac{1}{4πϵ_0}=k\) )

(1).\(\left(\frac{5}{8}\right)\)qK

(2). \(\left(\frac{8}{5}\right)\)qK

(3). \(\left(\frac{8}{3}\right)\)qK

(4). \(\left(\frac{3}{8}\right)\)qK

15. According to Gauss law of electrostatics, electric flux through a closed surface depends on :

(1).the area of the surface

(2). the quantity of charges enclosed by the surface

(3). the shape of the surface

(4). the volume enclosed by the surface

16. A charge Q µC is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit) :

(1).\(\frac{Q}{ \epsilon_0}\,×\,10^{-6}\)

(2). \(\frac{2Q}{3\epsilon_0}\,×\,10^{-3}\)

(3). \(\frac{Q}{6\epsilon_0}\,×\,10^{-3}\)

(4). \(\frac{Q}{6\epsilon_0}\,×\,10^{-6}\)

17. If a conducting sphere of radius R is charged. Then the electric field at a distance r (r>R) from the centre of the sphere would be, (V = potential on the surface of the sphere)

(1).\(rV/R^2 \)

(2). \(R^2V/r^3\)

(3). \(RV/r^2\)

(4). \(V/r\)

18. The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If C is its initial capacitance, its final capacitance is equal to :

(1).\(\frac{C}{4}\)

(2). \(2C\)

(3). \(\frac{C}{2}\)

(4). \(4C\)

19. The effective capacitances of two capacitors are 3 µF and 16 µF, when they are connected in series and parallel respectively. The capacitance of two capacitors are:

(1).1.2 µF, 1.8 µF

(2). 10 µF, 6 µF

(3). 8 µF, 8 µF

(4). 12 µF, 4 µF

20. Six charges +q, −q, +q, −q, +q and −q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q₀ to the centre of the hexagon from infinity is: (ε₀ - permittivity of free space )

(1).\(\frac{-q^2}{4πε_0d}\left(6-\frac{1}{\sqrt{2}}\right)\)

(2). Zero

(3). \(\frac{-q^2}{4πε_0d}\)

(4). \(\frac{-q^2}{4πε_0d}\left(3-\frac{1}{\sqrt{2}}\right)\)

21. The angle between the electric lines of force and the equipotential surface is

(1).\(0^\circ \)

(2). \(45^\circ \)

(3). \(90^\circ \)

(4). \(180^\circ \)

22. Two hollow conducting spheres of radii R₁ and R₂ (R₁ ≫ R₂) have equal charges. The potential would be

(1).More on bigger sphere

(2). More on smaller sphere

(3). Equal on both the spheres

(4). Dependent on the material property of the sphere

23. Two point charges −q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R (R ≫ L) varies as:

(1).\(\frac{1}{R^2}\)

(2). \(\frac{1}{R^3}\)

(3). \(\frac{1}{R^4}\)

(4). \(\frac{1}{R^6}\)

24. A capacitor of capacitance C = 900pF is charged fully by 100V battery B as shown in figure (a). Then it is disconnected from the battery and connected to another uncharged capacitor of capacitance C = 900pF as shown in figure (b). The electrostatic energy stored by the system (b) is

(1).4.5 × 10⁻⁶ J

(2). 3.25 × 10⁻⁶ J

(3). 2.25 × 10⁻⁶ J

(4). 1.5 × 10⁻⁶ J

25. A dipole is placed in an electric field as shown. In which direction will it move?

(1).Towards the left as its potential energy will increase.

(2). Towards the right as its potential energy willdecrease.

(3). Towards the left as its potential energy will decrease.

(4). Towards the right as its potential energy will increase.

26. The equivalent capacitance of the combination shown in the figure is

(1).3C

(2). 2C

(3). \(\frac{C}{2}\)

(4). \(\frac{3C}{2}\)

27. Two charged spherical conductors of radius R₁ and R₂ are connected by a wire. Then the ratio of surface charge densities of the spheres (σ₁/σ₂) is

(1).\(\frac{R_1}{R_2}\)

(2). \(\frac{R_2}{R_1}\)

(3). \(\sqrt{\frac{R_!}{R_2}}\)

(4). \(\frac{R_1^2}{R_2^2}\)

28. A parallel plate capacitor has a uniform electric field ' \(\vec{F}\) ' in the space between the plates. If the distance between the plates is ' d ' and the area of each plate is ' A ', the energy stored in the capacitor is ( ε₀ = permittivity of free space)

(1).\(\frac{1}{2}ε_0E^2\)

(2). \(ε_0E Ad\)

(3). \(\frac{1}{2}ε_0E^2Ad\)

(4). \(\frac{E^2Ad}{ε_0}\)

29. Polar molecules are the molecules

(1).Having zero dipole moment

(2). Acquire a dipole moment only in the presence of electric field due to displacement of charges

(3). Acquire a dipole moment only when magnetic field is absent

(4). Having a permanent electric dipole moment

30. Twenty seven drops of same size are charged at 220 V each. They combine to form a bigger drop. Calculate the potential of the bigger drop.

(1).660 V

(2). 1320 V

(3). 1520 V

(4). 1980 V

31. A spherical conductor of radius 10 cm has a charge of \(3.2 × 10_{−7} C\) distributed uniformly. What is the magnitude of electric field at a point 15cm from the centre of the sphere? ( \(1 ∕ 4π \epsilon_0 = 9 × 10^9 N m^2/C^2\))

(1).\(1.28 × 10^5\,N ∕ C \)

(2). \(1.28 × 10^6\, N ∕ C \)

(3). \(1.28 × 10^7\, N ∕ C \)

(4). \(1.28 × 10^4\ ,N ∕ C \)

32. In a certain region of space with volume 0.2 m³, the electric potential is found to be 5V throughout. The magnitude of electric field in this region is:

(1).0.5N ∕ C

(2). 1N ∕ C

(3). 5N ∕ C

(4). zero

33. A short electric dipole has a dipole moment of 16 × 10⁻⁹Cm. The electric potential due to the dipole at a point at a distance of 0.6m from the centre of the dipole, situated on a line making an angle of \(60^\circ\) with the dipole axis is : \(\left(\frac{1}{4πϵ0} = 9 × 10^9 Nm^2/C^2\right)\)

(1).200V

(2). 400V

(3). zero

(4). 50V

34. The capacitance of a parallel plate capacitor with air as medium is 6µF . With the introduction of a dielectric medium, the capacitance becomes 30µF. The permittivity of the medium is:
(\(E_0 = 8.85 × 10^{−12}\,C^2N^{−1}m^{−2}\))

(1).\( 1.77×10^{−12}\, C^2N^{−1}m^{−2}\)

(2). \(0.44×10^{−10}\, C^2N^{−1}m^{−2}\)

(3). \(5.00\, C^2 N^{−1}m^{−2}\)

(4). \(0.44×10^{−13}\, C^2N^{−1}m^{−2}\)

35. A hollow metal sphere of radius R is uniformly charged. The electricfield due to the sphere at a distance r from the centre

(1).decreases as r increases for r < R and for r > R

(2). increases as r increases for r < R and for r > R

(3). zero as r increases for r < R, decreases as r increases for r > R

(4). zero as r increases for r < R, increases as r increases for r > R

36. Two point charges A and B, having charges +Q and −Q respectively, are placed at certain distance apart and force acting between them is F . If 25% charge of A is transferred to B, then force between the charges becomes

(1).\(\frac{4F}{3}\)

(2). \(F\)

(3). \(\frac{9F}{16}\)

(4). \(\frac{16F}{9}\)

37. Two parallel infinite line charges with linear charge densities +λ C/m and -λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?

(1).\(\frac{λ}{2πε_0R}N ∕ C\)

(2). zero

(3). \(\frac{2λ}{πε_0R}N ∕ C\)

(4). \(\frac{λ}{πε_0R}N ∕ C\)

38. Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densitieson them?

(1).\( σ_1 =\frac{5}{6}σ, \,\,σ_2 =\frac{5}{2}σ\)

(2). \( σ_1 =\frac{5}{2}σ,\,\, σ_2 =\frac{5}{6}σ\)

(3). \( σ_1 =\frac{5}{2}σ, \,\,σ_2 =\frac{5}{3}σ\)

(4). \( σ_1 =\frac{5}{3}σ, \,\,σ_2 =\frac{5}{6}σ\)

39. Two identical capacitors C₁ and C₂ of equal capacitance are connectedshown in the circuit. Terminals a and b of the key k are connected to charge capacitor C₁ using battery of emf V volt. Now disconnecting a and b the terminals b and c are connected. Due to this, what will be the percentage loss of energy?

(1).75%

(2). 0%

(3). 50%

(4). 25%

40. An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electricfield is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is

(1).smaller

(2). 5 times greater

(3). 10 times greater

(4). equal

41. The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

(1).Independent of the distance between the plates

(2). Linearly proportional to the distance between the plates

(3). Proportional to the square root of the distance between the plates

(4). Inversely proportional to the distance between the plates

42. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field \(\vec{E}\). Due to the force q \(\vec{E}\), its velocity increases from 0 to 6 ms⁻¹ in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively

(1).2 ms⁻¹ , 4ms⁻¹

(2). 1ms⁻¹ , 3ms⁻¹

(3). 1ms⁻¹ , 3.5ms⁻¹

(4). 1.5ms⁻¹ , 3ms⁻¹

43. A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

(1).decreases by a factor of 2

(2). remains the same

(3). increases by a factor of 2

(4). increases by a factor of 4

44. Suppose the charge of a proton and an electron differ slightly. One of them is -e, the other is (e+Δe). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δe is of the order of
[given ma of hydrogen m_h = 1.67 × 10⁻²⁷kg ]

(1).10⁻²³ C

(2). 10⁻³⁷ C

(3). 10⁻⁴⁷ C

(4). 10⁻²⁰ C

45. The diagrams below show regions of equipotential. A positive charge is moved from A to B in each diagram.

(1).In all the four cases the work done is the same.

(2). Minimum work is required to move q in figure (I)

(3). Maximum work is required to move q in figure (II)

(4). Maximum work is required to move q in figure (III)

46. A capacitor of 2 μF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is

(1).75%

(2). 80%

(3). 0%

(4). 20%

47. Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d << I) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as

(1).v ∝ x^-1/2

(2). v ∝ x⁻¹

(3). v ∝ x^1/2

(4). v ∝ x

48. An electric dipole is placed at an angle of \(30^\circ\) with an electric field intensity 2 × 10⁵N C⁻¹. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is

(1).8 mC

(2). 2 mC

(3). 5 mC

(4). 7 µC

49. A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k₁, k₂, k₃ and k₄ as shown in the figure. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by

(1).\(k = k_1+ k_2 + k_3 + 3k_4\)

(2). k = \(\frac{2}{3}\left(k_1 + k_2 + k_3\right)\) + 2k₄

(3). \(\frac{2}{k}\,=\,\frac{3}{k_1 + k_2 + k_3}\,+\,\frac{1}{k_4}\)

(4). \(\frac{1}{k}\,=\,\frac{1}{k_1}\,+\,\frac{1}{k_2}\,+\,\frac{1}{k_3}\,+\,\frac{3}{2k_4}\)

50. The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by

(1).\(4πε_0Aa^3\)

(2). \(ε_0Aa^3\)

(3). \(4πε_0Aa^2\)

(4). \(Aε_0a^2\)

51. A parallel plate air capacitor of capacitance C is connected to a cell ofemf V and then disconnected from it. A dielectric slab of dielectricconstant K, which can just fill the air gap of the capacitor, is nowinserted in it. Which of the following is incorrect?

(1).The change in energy stored is \(\frac{1}{2}CV^2\left(\frac{1}{k}-1\right)\)

(2). The charge on the capacitor is not conserved.

(3). The potential difference between the plates decreases K times.

(4). The energy stored in the capacitor decreases K. times.

52. A parallel plate air capacitor of capacitance C is connected to a cell ofemf V and then disconnected from it. A dielectric slab of dielectric constant K, which can just fill the air gap of the capacitor, is now inserted in it. Which of the following is incorrect ?

(1).The energy stored in the capacitor decreases K times.

(2). The change in energy stored is \(\frac{1}{2}CV^2\left(\frac{1}{k}-1\right)\)

(3). The charge on the capacitor is not conserved.

(4). The potential difference between the platesdecreases K times.

53. If potential (in volts) in a region is expressed as V (x, y, z) = 6xy - y + 2yz, the electric field (in N/C) at point (1, 1, 0) is

(1).\(-\left(2\hat{i}+3\hat{j}+\hat{k}\right)\)

(2). \(-\left(6\hat{i}+9\hat{j}+\hat{k}\right)\)

(3). \(-\left(3\hat{i}+5\hat{j}+3\hat{k}\right)\)

(4). \(-\left(6\hat{i}+5\hat{j}+2\hat{k}\right)\)

54. Two thin dielectric slabs of dielectric constants K₁ and K₂ (K₁ < K₂) arevinserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distanced as measured from plate P is correctly shown by

(1).

(2).

(3).

(4).

55. The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constants \(\text{K}_1\, \text{and}\, \text{K}_2\) with thickness \(\displaystyle \frac{3}{8}\text{d}\) and \(\displaystyle \frac{d}{2}\), respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between plates.
If \(\text{K}_1\,=\,1.25\, \text{K}_2\), the value of \(\text{K}_1\) is:

(1).1.33

(2). 2.66

(3). 2.33

(4). 1.60