Electrostatic Potential and Capacitance · Question 13

There are three concentric conducting spherical shells A, B and C of radii a, b and c respectively (c > b > a) and they are charged with charges q1, q2 and q3 respectively. The potentials of the spheres A, B and C respectively, are :

1. 14 0 ( q1a + q2b + q3c ), 14 0 ( q1 + q2 + q3b ), 14 0 ( q1 + q2 + q3c )
2. 14 0 ( q1 + q2 + q3a ), 14 0 ( q1 + q2 + q3b ), 14 0 ( q1 + q2 + q3c )
3. 14 0 ( q1 + q2 + q3a ), 14 0 ( q1 + q2b + q3c ), 14 0 ( q1a + q2b + q3c )
4. 14 0 ( q1a + q2b + q3c ), 14 0 ( q1 + q2b + q3c ), 14 0 ( q1 + q2 + q3c )

Three parallel plate capacitors each with area A and separation d are filled with two dielectrics (k1 and k2) in the following fashion. Which of the following is true? (k1 > k2) [figure]

1. CC > CB > CA
2. CB > CC > CA
3. CA > CC > CB
4. CC > CA > CB

The space between the plates of a parallel plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants K1 = 2, K2 = 3 and K3 = 5 (as shown in figure). If new capacitance is n3C then the value of n is . [figure]

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25\% more charge from the battery. The dielectric constant of mica is

1. 1.0
2. 2.5
3. 1.5
4. 2.0

Two charges 7 and -2 are placed at (-9, 0, 0) cm and (9, 0, 0) cm respectively in an external field E = Ar2 r, where A = 9 105 N m2 C-1. Considering the potential at infinity is 0, the electrostatic energy of the configuration is J.

1. 49.3
2. 1.4
3. 24.3
4. -90.7

Electric field in a region is given by E = Ax i + By j, where A = 10 V/m2 and B = 5 V/m2. If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is V.

1. 1000
2. 0
3. 2000
4. 500

Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field ( E) at the center O of the pentagon due to these five positive charges are : [figure]

1. V = 5q4 0 r and E = 5 3q8 0 r2 r
2. V = 5q4 0 r and E = 0
3. V = 0 and E = 0
4. V = 5q4 0 r and E = 5q4 0 r2 r

Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :

1. 1 : 32/3
2. 32/3 : 1
3. 1 : 31/3
4. 1 : 22/3

A capacitor P with capacitance 10 10-6 F is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance 20 10-6 F. The charge on capacitor Q when equilibrium is established will be 10-5 C (assume capacitor Q does not have any charge initially), the value of is .

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ( 13 )rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

1. 3CK2(2K+1)2
2. 4KC3K-1
3. CK2+K
4. 3KC2K+1