A charged Particle q is shot towards another charged particle Q which is fixed , with a speed v. It approaches Q up to a closet distance r and then returns, If q were given a speed 2 v the n find the closet distance of approach.

Two Capacitors of capacitace 6\(\mu \)F and 12\(\mu \)F ae connnected in series with tha battery the volatage across the 6\(\mu \)F capacitor is 2 volt, Compute the total battery voltage.

There is a sphere of radius 20 cm. What charge should be given to the sphere so that it acquires a surface charge density of \({ 3 }/{ \pi }{ cm }^{ -2 }\)?

A regular hexagon of side 10 cm has a charge 5\(\mu\) C at each of its vertices. Calculate the potential at the centre of the hexagon.

The electric field intensity and potential at a point due to a point charge are 36 N/C and 18 J/C respectively. Calculate
(i) magnitude and
(ii) position of the charge  from the point.

A spherical Gaussian surface encloses a charge of \(8.85\times {{10}^{-8}}C.\)
(i) Calculate the electric flux passing through the surface.
(ii) If the radius of the Gaussian surface is doubled, how  would the flux change?

Two point charges \(+4\mu C\) and \(-6\mu C\) are separated by a distance of 20cm in air. At what point on the line joining the two charges is the electric potential zero?

An electric dipole with dipole moment \(4\times{{10}^{-9}}CM\) is aligned at 30⁰ with direction of a uniform electric field of magnitude \(5\times{{10}^{4}}NC^{-1}.\)Calculate the magnitude of  the torque acting on the dipole.

Calculate the electric field strength which is required to just support a water drop of mass 10^-3kg and having a charge \(1.6\times 10^{-19}C\)

Two charges each of \(1\mu C\) but opposite in sign are 1cm apart. Calculate electric field at a point distant 10cm from the mid point on axial line of the dipole.

Two charges \(+20\mu C\) and \(-20\mu C\) are held 1cm apart. Calculate the electric field at a point on the equatorial line at a distance of 50cm from the centre of the dipole.

The potential difference between a cloud and the Earth is 107V. Calculate the amount of energy dissipated when the charge of 100 is transferred from the cloud to the ground due to lighting bolt.