Electrostatic Potential and Capacitance

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of 1 μF when the space between the plates is filled with an insulating material of resistivity 1 1013 Ωm and resistance 17.7 1014 Ω. Relative permittivity of the insulating material is 107. The value of is . (Take permittivity of free space =8.85 10-12 F/m)

A three coulomb charge moves from the point (0, -2, -5) to the point (5, 1, 2) in an electric field expressed as E=2x i+3y2 j+4 k N/C. The work done in moving the charge is J.

The electric potential as a function of x, y is given by V=5 (x2-y2 ) V. The electric field at a point (2, 3) m is V/m.

1. (-20 i+30 j )
2. (20 i-30 j )
3. (20 i+45 j )
4. (-4 i+6 j )

A sphere of capacitance 100 pF is charged to a potential of 100 V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is 10-7 J. The value of is . (combined capacitance of spheres is 200 pF)

1. 5
2. 52
3. 72
4. 92

A parallel plate air capacitor is connected to a battery. The plates are pulled apart at uniform speed v. If x is the separation between the plates at any instant, then the time rate of change of electrostatic energy of the capacitor is proportional to x , where is .

1. -2
2. 1
3. -1
4. 2

From the circuit given below, the capacitance between terminals A and B shown in the circuit is μF. (take C1=C2=C3=1 μF and C4=2 μF.) [figure]

1. 2
2. 7/2
3. 7/3
4. 5/2

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). 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 but (R) is NOT the correct explanation of (A)
3. (A) is true but (R) is false
4. (A) is false but (R) is true

A parallel plate air capacitor has a capacitance C. When it is half filled as shown in figure with a dielectric constant K=5, the percentage increase in the capacitance is . [figure]

1. 33.34
2. 66.67
3. 200
4. 400

Two charged conducting spheres S1 and S2 of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on S1 and S2 spheres are ES1 and ES2 respectively. The value of ES1ES2 is .

1. 32
2. 23
3. 49
4. 94

Two metal plates (A, B) are kept horizontally with separation of ( 12 ) cm, with plate A on the top. An atomizer jet sprays oil (density 1.5 g/cm3) droplets of radius 1 mm horizontally. All oil droplets carry a charge 5 nC. The potentials VA and VB are required on plates A and B respectively in order to ensure the droplets do not descend. The values of VA and VB are . (Neglect the air resistance to the droplets and take g=10 m/s2)

1. 100 V and 580 V
2. 580 V and 100 V
3. 60 V and 400 V
4. 0 V and -200 V

Two point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is . 14 0 = 9 109 N m2/C2

1. 3.3
2. 27
3. 2.7
4. 5.4

Which one of the following is not a measurable quantity?

1. Resistance
2. Voltage difference
3. Displacement current
4. Voltage

Identify the correct statements : Choose the correct answer from the options given below :

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

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

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