Electrostatic Potential and Capacitance

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

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 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

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

Three parallel plate capacitors C1, C2 and C3 each of capacitance 5 are connected as shown in figure. The effective capacitance between points A and B, when the space between the parallel plates of C1 capacitor is filled with a dielectric medium having dielectric constant of 4, is : [figure]

1. 9
2. 30
3. 7.5
4. 22.5

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constants 1 and 2, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are C1 and C2 respectively, then C1C2 is: First Configuration [figure] Second Configuration [figure]

1. 0( 1 + 2)2
2. 1 22( 1 + 2)2
3. 4 1 2( 1 + 2)2
4. 1 2 1 + 2

The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell respectively, are:

1. 0 V, 120 V, 40 V
2. 120 V, 120 V, 80 V
3. 40 V, 40 V, 80 V
4. 0 V, 0 V, 80 V

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)

1. 600
2. 100
3. 400
4. 200