A ring of charge with radius $0.5\, m$ having a $0.02\, m$ gap, carries a charge of $+1\, C$. The field at the centre is

$(a)$ Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where $E =0$ ) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.

$(b)$ Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance apart.

Is electric field scalar or vector ? Why ?

What is the magnitude of a point charge which produces an electric field of $2\, N/coulomb$ at a distance of $60\, cm$ $(1/4\pi {\varepsilon _0} = 9 \times {10^9}\,N - {m^2}/{C^2})$

A charged particle of mass $5 \times {10^{ - 5}}\,kg$ is held stationary in space by placing it in an electric field of strength ${10^7}\,N{C^{ - 1}}$ directed vertically downwards. The charge on the particle is

The electric field in a region is radially outward and at a point is given by $E=250 \,r V / m$ (where $r$ is the distance of the point from origin). Calculate the charge contained in a sphere of radius $20 \,cm$ centred at the origin ......... $C$