Electrostatic Potential and Capacitance · Question 39

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.