The electric field at a distance $r$ from the centre in the space between two concentric metallic spherical shells of radii $r_1$ and $r_2$ carrying charges $Q_1$ and $Q_2$ respectively is $(r_1 < r < r_2)$.

$A$ non-conducting solid sphere has radius $R$ and uniform charge density. $A$ spherical cavity of radius $\frac{R}{4}$ is hollowed out of the sphere. The distance between the center of the sphere and the center of the cavity is $\frac{R}{2}$. If the charge of the sphere is $Q$ after the creation of the cavity and the magnitude of the electric field at the center of the cavity is $E = K \left( \frac{Q}{4 \pi \epsilon_0 R^2} \right)$,determine the approximate value of $K$.

The figure shows a hollow hemisphere of radius $R$ in which two charges $3q$ and $5q$ are placed symmetrically about the centre $O$ on the planar surface. The electric flux over the curved surface is

An infinitely long thin straight wire has a uniform charge density of $\frac{1}{4} \times 10^{-2} \text{ C/m}$. What is the magnitude of the electric field at a distance of $20 \text{ cm}$ from the axis of the wire?

Two infinitely long thin straight parallel wires are kept at a perpendicular distance of $2R$,having uniform linear charge densities $+\lambda$ and $-\lambda$ respectively. The magnitude of the electric field at the midpoint between the two wires will be . . . . . . .

Let $P(r) = \frac{Q}{\pi R^4} r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $P$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is