A point charge \(+q\) is kept at the center of the curvature of thin semicircular wire of length \(l\) as shown. The wire has uniformly distributed charge \(-q\) on it. The dipole moment of the system is

                  
1. \(\dfrac{2ql}{\pi^2}\)
2. \(\dfrac{2ql}{\pi}\)
3. \(\dfrac{\pi ql}{2}\)
4. zero

A conducting body has a cavity in its as shown in the diagram below. A point charge q is held at the centre of the cavity. The electric flux linked with the closed surface S (shown dotted) is

1.  $\frac{q}{{\epsilon }_0}$

2.  $\frac{q}{2{\epsilon }_0}$

3.  $\frac{q}{6{\epsilon }_0}$

4.  Zero

A neutral bubble made of soap solution has radius R. If some negative charge is given which gets distributed uniformly on the surface of the bubble, the radius of the bubble becomes R' then

1.  R' > R

2.  R' = R

3.  R' < R

4.  R' = 0.5 R

A large non-conducting sheet \(S\) is given a uniform charge density. Two uncharged small, metal rods \(A\) and \(B\) are placed near the sheet as shown in the following diagram. Choose the incorrect option:

1.  \(S\) attracts \(A\)

2.  \(S\) attracts \(B\)

3.  \(A\) attracts \(B\)

4.  \(S\) repels \(A\)

An electric dipole is placed at the centre of a sphere. Which of the following statements is correct?

A particle with charge +ve and mass m is projected with velocity v in the opposite direction of a uniform electric field E as shown in the figure in a gravity-free space. After what time the velocity will become -v?

1.  $\frac{mv}{2<mspace\; width="1em"></mspace>qE}$

2.  $\frac{mv}{qE}$

3.  $\frac{2<mspace\; width="1em"></mspace>mv}{qE}$

4.  $\frac{4<mspace\; width="1em"></mspace>mv}{qE}$

Which of the following statements is correct about a dipole in a non-uniform field?

1.  Torque is always nonzero

2.  Net force may be nonzero

3.  Torque is always zero

4.  Net force is always zero

A particle of mass m has a charge $q_0$ when it is at rest. When the particle moves with speed v, the charge on the particle will become (c is the velocity of light in vacuum)

1.  $\frac{q_{0}v}{c}$

2.  $\frac{q_{0}c}{v}$

3.  $\frac{q_0}{\sqrt{1-\frac{v^2}{c^2}}}$

4.  $q_0$

Starting from rest an electron moves through a small distance in a uniform electric field of magnitude $2<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^4<mspace\; width="1em"></mspace>N{C}^{-1}$. The direction of the field is reserved keeping the magnitude unchanged and a proton moves through the same distance. The time of motion will be

1.  Same in both cases

2.  More in the case of an electron

3.  More in the case of proton

4.  Independent of charge

A source charge Q is kept at a distance of 3 km from a test charge $q_0$. If Q is displaced slightly, then the change in the electric field detected by $q_0$ will be after

1.  10 s

2.  10 ms

3.  10 $\mu$s

4.  10 ns