Three identical point charges, as shown are placed at the vertices of an isosceles right angled triangle. Which of the numbered vectors coincides in direction with the electric field at the mid-point $M$ of the hypotenuse

A ring of radius $R$ is charged uniformly with a charge $+\,Q$ . The electric field at a point on its axis at a distance $r$ from any point on the ring will be

$(a)$ 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.

A hollow sphere of charge does not produce an electric field at any

A half ring of radius $R$ has a charge of $\lambda$ per unit length. The electric force on $1\, C$ charged placed at the centre is

A small metal ball is suspended in a uniform electric field with the help of an insulated  thread. If high energy $X$ -ray beam falls on the ball, then the ball