The charge distribution along the semi-circular arc is non-uniform . Charge per unit length $\lambda $ is given as $\lambda  = {\lambda _0}\sin \theta $ , with $\theta $ measured as shown in figure. $\lambda_0$ is a positive constant. The radius of arc is $R$ . The electric field at the center $P$ of semi-circular arc is $E_1$ . The value of $\frac{{{\lambda _0}}}{{{ \in _0}{E_1}R}}$ is

An oil drop carries six electronic charges, has a mass of $1.6 \times 10^{-12} g$ and falls with a terminal velocity in air. The magnitude of vertical electrical electric field required to  make the drop move upward with the same speed as was formely moving is ……..$kN/C$

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 positively charged ball hangs from a silk thread. We put a positive test charge ${q_0}$ at a point and measure $F/{q_0}$, then it can be predicted that the electric field strength $E$

A uniformly charged disc of radius $R$ having surface charge density $\sigma$ is placed in the ${xy}$ plane with its center at the origin. Find the electric field intensity along the $z$-axis at a distance $Z$ from origin :-