If the potential at the centre of a uniformly charged ring is $V_0$,then the electric field at its centre will be (assume radius $= R$):

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

$A$ point charge $q$ is placed at the origin. Let $E_A, E_B,$ and $E_C$ be the electric fields at three points $A(1, 2, 3)$,$B(1, 1, -1)$,and $C(2, 2, 2)$ respectively due to the charge $q$. Then,the correct relations among them are:
$1. E_A \perp E_B$
$2. E_A \parallel E_C$
$3. |E_B| = 4|E_C|$
$4. |E_B| = 8|E_C|$

The charge distribution along the semi-circular arc is non-uniform. The charge per unit length $\lambda$ is given as $\lambda = \lambda_0 \sin \theta$,with $\theta$ measured as shown in the figure. $\lambda_0$ is a positive constant. The radius of the arc is $R$. The electric field at the center $P$ of the semi-circular arc is $E_1$. The value of $\frac{\lambda_0}{\epsilon_0 E_1 R}$ is

Two charges $+Q$ and $-2 Q$ are located at points $A$ and $B$ on a horizontal line as shown below. The electric field is zero at a point which is located at a finite distance:

$A$ thin conducting ring of radius $R$ is given a charge $+Q.$ The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E.$ The electric field at the centre due to the charge on the part $ACDB$ of the ring is