Electrostatic Potential and Capacitance

Three infinitely long wires with linear charge density are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

1. (x2 + y2)(y2 + z2)(z2 + x2) = constant
2. xyz = constant
3. xy + yz + zx = constant
4. (x + y)(y + z)(z + x) = constant

Two capacitors C1 and C2 are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are U1 and U2, respectively. Which of the given statements is true? [figure]

1. C2 > C1, U2 > U1
2. C1 > C2, U1 > U2
3. C2 > C1, U2 < U1
4. C1 > C2, U1 < U2

A particle of mass 'm' and charge 'q' is fastened to one end 'A' of a massless string having equilibrium length l, whose other end is fixed at point 'O'. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is [figure]

1. qEl2m
2. qEl4m
3. qElm
4. 2qElm

A parallel plate capacitor of capacitance 1 μF is charged to a potential difference of 20 V. The distance between plates is 1 μm. The energy density between plates of capacitor is :

1. 1.8 103 J/m3
2. 2 102 J/m3
3. 2 10-4 J/m3
4. 1.8 105 J/m3

An electric dipole of dipole moment 6 10-6 C m is placed in uniform electric field of magnitude 106 V/m. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be J.

Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and 0 is the permittivity of free space between the plates, then potential energy stored in the capacitor is

1. 0E2Ad
2. 34 0E2Ad
3. 14 0E2Ad
4. 12 0E2Ad

A parallel plate capacitor was made with two rectangular plates, each with a length of l=3 cm and breadth of b=1 cm. The distance between the plates is 3 . Out of the following, which are the ways to increase the capacitance by a factor of 10 ? Choose the correct answer from the options given below:

1. C only
2. A only
3. B and D only
4. C and E only

[figure] In the first configuration (1) as shown in the figure, four identical charges (q0) are kept at the corners A, B, C and D of square of side length 'a'. In the second configuration (2), the same charges are shifted to mid points G, E, H and F, of the square. If K= 14 0, the difference between the potential energies of configuration (2) and (1) is given by :

1. Kq02a (4-2 2 )
2. Kq02a (4 2-2 )
3. Kq02a (3- 2 )
4. Kq02a (3 2-2 )

Two point charges -4 and 4 , constituting an electric dipole, are placed at (-9,0,0) cm and (9,0,0) cm in a uniform electric field of strength 104 N C-1. The work done on the dipole in rotating it from the equilibrium through 180 is :

1. 18.4 mJ
2. 12.4 mJ
3. 16.4 mJ
4. 14.4 mJ

Two charges 7 and -4 are placed at (-7 cm,0,0) and (7 cm,0,0) respectively. Given, 0=8.85 10-12 C2 N-1 m-2, the electrostatic potential energy of the charge configuration is :

1. -2.0 J
2. -1.5 J
3. -1.2 J
4. -1.8 J