A conducting sphere of radius \(10\) cm has an unknown charge. If the electric field, \(20\) cm from the centre of the sphere is \(1.5\times10^3\) N/C and points radially inward, what is the net charge on the sphere?
1. \(-5.70\) nC
2. \(-6.67\) nC
3. \(6.67\) nC
4. \(5.70\) nC

A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of $80.0 \mu C/m^2$. The charge on the sphere is:

1. 2 .077 × 10^-3 C
2. 2. 453 × 10^-3C
3. 1. 447 × 10^-3C
4. 3. 461 × 10^-3C

 

An infinite line charge produces a field of \(9\times10^{4}~\text{N/C}\) at a distance of \(2~\text{cm}\). The linear charge density is:
1. \(0.1~\mu\text{C/m}\)
2. \(100~\mu\text{C/m}\)
3. \(1.0~\mu\text{C/m}\)
4. \(10~\mu\text{C/m}\)

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 x 10^-22 C/m². The electric field between the plates is: 

1. 0.96 × 10^-10   N/C
2. 1.92 × 10^{- 10}   N/C
3. 0
4. 3.84 × 10^-10   N/C

An oil drop of 12 excess electrons is held stationary under a constant electric field of $2.55\times {10}^{-4} N C^{-1}$. The density of the oil is $1.26 g c{m}^{-3}$. The radius of the drop is:

1. \(9.82\times10^{-4}\) mm
2. \(9.82\times10^{-7}\) mm
3. \(8.92\times10^{-4}\) mm
4. \(8.92\times10^{-7}\) mm

 

Which among the curves shown in the figure represents electrostatic field lines?
 

1.		2.
3.		4.

In a certain region of space, the electric field is along the z-direction throughout. The magnitude of the electric field is, however, not constant but increases uniformly along the positive z-direction, at the rate of 10⁵ NC^-1 per meter. What is the torque experienced by a system having a total dipole moment equal to ${10}^{-7}$ $\mathrm{C-}m$ in the negative z-direction? 

A hollow charged conductor has a tiny hole cut into its surface. The electric field in the hole is:
1. \(\left(\frac{3 \sigma}{\varepsilon_0}\right) \widehat{n}\)
2. \(\left(\frac{2 \sigma}{\varepsilon_0}\right) \widehat{n}\)
3. \(\left(\frac{\sigma}{2 \varepsilon_0}\right) \widehat{n}\)
4. \(\left(\frac{\sigma}{\varepsilon_0}\right) \widehat{n}\)

A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along the x-axis with speed $v_x$ (as shown in the figure). The length of the plate is L and a uniform electric field E is maintained between the plates. The vertical deflection of the particle at the far edge of the plate is:

             
1. \(\frac{2 q E L^2}{3 m\left(v_x\right)^2}\)
2. \(\frac{2 q E L^2}{m\left(v_x\right)^2}\)
3. \(\frac{3 q E L^2}{2 m\left(v_x\right)^2}\)
4. \(\frac{q E L^2}{2 m\left(v_x\right)^2}\)

A spherical conducting shell of inner radius $r_1$ and outer radius $r_2$ has a charge Q. A charge q is placed at the center of the shell. The surface charge density on the outer surfaces of the shell is: