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

A charged water drop whose radius is $0.1\,\mu m$ is in equilibrium in an electric field. If charge on it is equal to charge of an electron, then intensity of electric field will be…….$N/C$ $(g = 10\,m{s^{ – 1}})$

The linear charge density on upper half of a segment of ring is $\lambda$ and at lower half, it is $-\lambda$. The direction of electrical field at centre $O$ of ring 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

An oil drop of $12$ excess electrons is held stationary under a constant electric field of $2.55 \times 10^{4}\; N\,C ^{-1}$ (Millikan's oil drop experiment). The density of the oil is $1.26 \;g \,cm ^{-3} .$ Estimate the radius of the drop. $\left(g=9.81\; m s ^{-2} ; e=1.60 \times 10^{-19}\; \,C \right)$