Electrostatic Potential and Capacitance · Question 56

The electric potential at a point (x, y, z) is given by V = -x2y - xz3 + 4 The electric field at that point is

1. E = i 2xy + j (x2 + y2) + k (3xz - y2)
2. E = i z3 + j xyz + k z2
3. E = i (2xy - z3) + j xy2 + k 3z2x
4. E = i (2xy + z3) + j x2 + k 3xz2

A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is

1. 12 0 E2
2. E2Ad 0
3. 12 0 E2Ad
4. 0 EAd

The electric potential at a point in free space due to charge Q coulomb is Q 1011 volts. The electric field at that point is

1. 4 0 Q 1020 volt/m
2. 12 0 Q 1022 volt/m
3. 4 0 Q 1022 volt/m
4. 12 0 Q 1020 volt/m

Charges +q and -q are placed at points A and B respectively which are a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is [figure]

1. qQ2 0L
2. qQ6 0L
3. - qQ6 0L
4. qQ4 0L

Two condensers, one of capacity C and other of capacity C/2 are connected to a V-volt battery, as shown in the figure. The work done in charging fully both the condensers is [figure]

1. 14CV2
2. 34CV2
3. 12CV2
4. 2CV2

A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates

1. increases
2. decreases
3. does not change
4. becomes zero

An electric dipole of moment p is lying along a uniform electric field E. The work done in rotating the dipole by 90 is

1. pE
2. 2pE
3. pE/2
4. 2pE

A network of four capacitors of capacity equal to C1 = C, C2 = 2C, C3 = 3C and C4 = 4C are connected to a battery as shown in the figure. The ratio of the charges on C2 and C4 is [figure]

1. 4/7
2. 3/22
3. 7/4
4. 22/3

As per the diagram a point charge +q is placed at the origin O. Work done in taking another point charge −Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is [figure]

1. zero
2. ( qQ4 0 1a2 ) 2a
3. ( -qQ4 0 1a2 ) 2a
4. ( qQ4 0 1a2 ) a 2

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is q34 0k, where k is [figure]

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