Two infinitely long parallel wires having linear charge densities $\lambda_1$ and $\lambda_2$ respectively are placed at a distance of $R$ meters. The force per unit length on either wire will be $(K = \frac{1}{4\pi\varepsilon_0})$.

Let $\rho (r) = \frac{Q}{\pi R^4} r$ be the volume 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:

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 $(r_1 < r < r_2)$.

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2 \sigma$. The force experienced by a point charge $+q$ placed at the midpoint between the two plates will be:

$A$ 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 $K$.

An early model for an atom considered it to have a positively charged point nucleus of charge $Ze$,surrounded by a uniform density of negative charge up to a radius $R$. The atom as a whole is neutral. For this model,what is the electric field at a distance $r$ from the nucleus?