Electrostatic Potential and Capacitance · Question 4

A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius R, having uniform positive charge density , as shown in the figure. The initial and final positions of the charge are marked by A and B at distance 2R and 3R respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is R2n 0. The value of n is : ( 0 is the permittivity of vacuum) [figure]

1. 18
2. 2
3. 6
4. 9

Consider a fixed uniformly charged insulating sphere with radius R and total charge +Q. A point charge -q (q Q) with mass m is released from rest at a distance of 3R from the centre of the charged sphere. When the point charge reaches the surface of the sphere, its speed is: ( 0 is the permittivity of vacuum, neglect gravitational forces).

1. Qq4 0 mR
2. 3Qq4 0 mR
3. 2Qq3 0 mR
4. Qq3 0 mR

A point charge Q is placed inside a cavity within a solid isolated conducting sphere. Consider points A, B and C as shown in the figure, where the magnitudes of the electric fields are EA, EB, EC, respectively. The points B and C are at the same distance from the center of the solid sphere. The correct option is : [figure]

1. EA 0, EB < EC
2. EA = 0, EB = EC
3. EA 0, EB = EC
4. EA = 0, EB > EC

The plates of a parallel plate capacitor are separated by d. Two slabs of different dielectric constant K1 and K2 with thickness 38d and d2, respectively are inserted in the capacitor. Due to this, the capacitance becomes two times larger than when there is nothing between the plates. If K1 = 1.25K2, the value of K1 is:

1. 1.60
2. 1.33
3. 2.66
4. 2.33

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 14 0 = 9 109 SI units) [figure]

1. 3 105
2. 1 105
3. 0.5 105
4. Zero

In the following circuit, the equivalent capacitance between terminal A and terminal B is : [figure]

1. 2
2. 1
3. 0.5
4. 4

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.

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then 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

A 12 pF 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

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