Electrostatic Potential and Capacitance · Question 22

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)

Two charges q1 and q2 are separated by a distance of 30 cm. A third charge q3 initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of q3 from C to D is given by q3 K4 0, the value of K is : [figure]

1. 6q2
2. 6q1
3. 8q1
4. 8q2

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 most appropriate answer from the options given below :

1. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
2. (A) is correct but (R) is not correct
3. Both (A) and (R) are correct and (R) is the correct explanation of (A)
4. (A) is not correct but (R) is correct

A parallel plate capacitor has charge 5 10-6 C. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is 4 10-6 C then the dielectric constant of the slab is .