A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are:

1. Zero and $\frac{Q}{4{\mathrm{\pi \epsilon }}_0{\mathrm{R}}^2}$

2. $\frac{Q}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$ and zero

3. $\frac{Q}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$ and $\frac{Q}{4{\mathrm{\pi \epsilon }}_0{\mathrm{R}}^2}$

4. Both are zero.

An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with the direction of the field. Assuming that the potential energy of the dipole to be zero when $\theta =90°$, the torque and the potential energy of the dipole will respectively be

1. $pE \sin \theta ,-pE \cos \theta$

2. $pE \sin \theta ,-2pE \cos \theta$

3. $pE \sin \theta , 2pE \cos \theta$

4. $pE \cos \theta ,-pE \sin \theta$

The diagrams below show regions of equipotential. 
 
A positive charge is moved from A to B in each diagram.

1. In all the four cases , the work done is the same

2. Minimum work is required to move q in figure(a)

3. Maximum work is required to move q in figure (b)

4. Maximum work is required to move q in figure (c)

A parallel plate capacitor of capacitance 20 $\mu$F is being charged by a voltage source whose potential is charging at the rate of 3 V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively:

1. zero, zero

2. zero, 60$\mu$A

3. 60$\mu$A, 60$\mu$A

4. 60$\mu$A, zero

A parallel plate condenser has a uniform electric field E (V/m) in the space between the plates. If the distance between the plates is d(m) and area of each plate is A(m²) , the energy (joule) stored in the condenser is

1.  $\frac{1}{2}\left({\mathrm{\epsilon }}_{\mathrm{o}}\right){\left(\mathrm{E}\right)}^2$

2.  $\frac{{\mathrm{E}}^2 \mathrm{Ad}}{{\mathrm{\epsilon }}_{\mathrm{o}}}$

3.  $\frac{1}{2}\left({\mathrm{\epsilon }}_{\mathrm{o}}\right) {\mathrm{E}}^2 \mathrm{Ad}$

4.  $\left({\mathrm{\epsilon }}_{\mathrm{o}}\right) \mathrm{EAd}$

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. decreases

2. does not change

3. becomes zero

4. increases

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

1. $2 C{V}^2$

2. $\frac{1}{4} C{V}^2$

3. $\frac{3}{4} C{V}^2$

4. $\frac{1}{2} C{V}^2$

An electric dipole of moment $\overrightarrow{p}$ is lying along a uniform electric field $\overrightarrow{E}$. The work done in rotating the dipole by 90 ° is :

1. $\sqrt{2}pE$

2. $\frac{2E}{2}$

3. 2pE

4. pE

The true statement is, on increasing the distance between the plates of a parallel plate condenser -

(1) The electric intensity between the plates will decrease

(2) The electric intensity between the plates will increase

(3) The electric intensity between the plates will remain unchanged

(4) The P.D. between the plates will decrease