Electrostatic Potential and Capacitance · Question 19

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

A point charge of 10-8 C is placed at origin. The work done in moving a point charge 2 from point A(4, 4, 2) m to B(2, 2, 1) m is J. ( 14 0 = 9 109 in SI units)

1. 30 10-6
2. 0
3. 15 10-6
4. 45 10-6

Consider two identical metallic spheres of radius R each having charge Q and mass m. Their centers have an initial separation of 4R. Both the spheres are given an initial speed of u towards each other. The minimum value of u, so that they can just touch each other is: (Take k = 14 0 and assume kQ2 > Gm2 where G is the Gravitational constant)

1. kQ24mR (1 + Gm2kQ2 )
2. kQ22mR (1 - Gm22kQ2 )
3. kQ22mR (1 - Gm2kQ2 )
4. kQ24mR (1 - Gm2kQ2 )

Two metal spheres of radius R and 3R have same surface charge density . If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere become 1 and 2, respectively. The ratio 1 2 is

1. 13
2. 19
3. 9
4. 3

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. In the light of the above statements, choose the correct answer from the options given below.

1. A is true but R is false
2. Both A and R are true and R is the correct explanation of A
3. Both A and R are true but R is NOT the correct explanation of A
4. A is false but R is true

Electric charge is transferred to an irregular metallic disk as shown in the figure. If 1, 2, 3 and 4 are charge densities at given points then, choose the correct answer from the options given below: [figure]

1. B and C Only
2. A and C Only
3. D and E Only
4. A, B and C Only

[figure] Space between the plates of a parallel plate capacitor of plate area 4 cm2 and separation of 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is pF. (Given 0 = 8.85 10-12 F/m)