A positive charge $q$ is placed in a spherical cavity made in a positively charged sphere. The centres of sphere and cavity are displaced by a small distance $\vec l $ . Force on charge $q$ is :
in the direction parallel to vector $\vec l $
in radial direction
in a direction which depends on the magnitude of charge density in sphere
direction can not be determined.
A solid ball of radius $R$ has a charge density $\rho $ given by $\rho = {\rho _0}\left( {1 - \frac{r}{R}} \right)$ for $0 \leq r \leq R$. The electric field outside the ball is
Obtain the expression of electric field by a straight wire of infinite length and with linear charge density $'\lambda '$.
A spherical conductor of radius $10\, cm$ has a charge of $3.2 \times 10^{-7} \,C$ distributed uniformly. What is the magnitude of electric field at a point $15 \,cm$ from the centre of the sphere?
$\left(\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} Nm ^{2} / C ^{2}\right)$
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $\left(\sigma / 2 \varepsilon_{0}\right) \hat{ n },$ where $\hat{ n }$ is the unit vector in the outward normal direction, and $\sigma$ is the surface charge density near the hole.
Two long thin charged rods with charge density $\lambda$ each are placed parallel to each other at a distance $d$ apart. The force per unit length exerted on one rod by the other will be $\left(\right.$ where $\left.k=\frac{1}{4 \pi \varepsilon_0}\right)$