The electric field at a place is given by $\overrightarrow{E} = E_0 \hat{i} \text{ V/m}$. $A$ particle of charge $+q_0$ moves from point $A(0, a)$ to point $B(a, 0)$ along a circular path as shown in the figure. Find the work done by the electric field in this motion.

Three charges $2q, -q$ and $-q$ are located at the vertices of an equilateral triangle. At the center of the triangle,

$A$ thin non-conducting ring of radius $r$ has a linear charge density $\lambda = \lambda_0 \cos \phi$,where $\lambda_0$ is a constant and $\phi$ is the azimuthal angle. The magnitude of the electric field strength at the centre of the ring is

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

Two non-conducting solid spheres of radii $R$ and $2R$,having uniform volume charge densities $\rho_1$ and $\rho_2$ respectively,touch each other. The net electric field at a distance $2R$ from the centre of the smaller sphere,along the line joining the centres of the spheres,is zero. The ratio $\frac{\rho_1}{\rho_2}$ can be;
$(A) -4$ $(B) -\frac{32}{25}$ $(C) \frac{32}{25}$ $(D) 4$

The magnitude of a point charge due to which the electric field $30 \ cm$ away has a magnitude of $2 \ N \ C^{-1}$ is: