A spherical conductor of radius \(10~\text{cm}\) has a charge of \(3.2 \times 10^{-7}~\text{C}\) distributed uniformly. What is the magnitude of the electric field at a point \(15~\text{cm}\) from the center of the sphere? \(\frac{1}{4\pi \varepsilon _0} = 9\times 10^9~\text{N-m}^2/\text{C}^2\)
1. \(1.28\times 10^{5}~\text{N/C}\)
2. \(1.28\times 10^{6}~\text{N/C}\)
3. \(1.28\times 10^{7}~\text{N/C}\)
4. \(1.28\times 10^{4}~\text{N/C}\)

The electric field at a point on the equatorial plane at a distance \(r\) from the centre of a dipole having dipole moment $\stackrel{}{}$\(\overrightarrow{P}\) is given by:
(\(r\gg\) separation of two charges forming the dipole, \(\epsilon_{0} =\) permittivity of free space) 
1. \(\overrightarrow{E}=\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{3}}\) 

2. \(\overrightarrow{E}=\frac{2\overrightarrow{P}}{\pi \epsilon _{0}r^{3}}\)

3. \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{2}}\)

4. \(\overrightarrow{E}=-\frac{\overrightarrow{P}}{4\pi \epsilon _{0}r^{3}}\)

The acceleration of an electron due to the mutual attraction between the electron and a proton when they are \(1.6~\mathring{A}\) apart is:
( \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9~ \text{Nm}^2 \text{C}^{-2}\) )

A sphere encloses an electric dipole with charges \(\pm3\times10^{-6}\) C. What is the total electric flux through the sphere?
1. \(-3\times10^{-6}\) N-m²/C
2. zero
3. \(3\times10^{-6}\) N-m²/C
4. \(6\times10^{-6}\) N-m²/C

The electric field at a distance \(\frac{3R}{2}\) from the centre of a charged conducting spherical shell of radius \(R\) is \(E\). The electric field at a distance \(\frac{R}{2}\) from the centre of the sphere is:
1. \(E\)
2. \(\frac{E}{2}\)
3. \(\frac{E}{3}\)
4. zero
 

A hollow conducting sphere of radius \(1~\text{m}\) is given a positive charge of \(10~\mu\text{C}\). The electric field at the centre of the hollow sphere will be:
1. \(60\times10^{3}~\text{Vm}^{-1}\)
2. \(90\times10^{3}~\text{Vm}^{-1}\)
3. zero
4. infinite

The electric field at centre \(O\) of a semicircle of radius \(a\) having linear charge density \(\lambda\) is given by:

     
1. \(\frac{2\lambda}{\epsilon_0 a}\)
2. \(\frac{\lambda\pi}{\epsilon_0 a}\)
3. \(\frac{\lambda}{2\pi \epsilon_0 a}\)
4. \(\frac{\lambda}{\pi \epsilon_0 a}\)
 

If a charge \(Q\) is situated at the corner of a cube, the electric flux passing through all six faces of the cube is:

Who evaluated the mass of electron indirectly with help of charge:
1. Thomson
2. Millikan
3. Rutherford
4. Newton

A charge \(q\) is placed in a uniform electric field \(E.\) If it is released, then the kinetic energy of the charge after travelling distance \(y\) will be:
1. \(qEy\)
2. \(2qEy\)
3. $\frac{qEy}{2}$
4. $\sqrt{qEy}$