A negative charge $Q$ is distributed uniformly in the volume of a sphere of radius $R$ and a point charge particle (may be negative or positive) is present on the surface of this sphere, then the variation of the escape velocity $\left(v_{\mathrm{s}}\right)$ of charge $q$ as a function of $q$ will be [neglect gravitational interaction]

A positive point charge $+Q$ is fixed in space. A negative point charge $-q$ of mass $m$ revolves around fixed charge in an elliptical orbit. The fixed charge$+Q$ is at one focus of the ellipse. The only force acting on the negative charge is the electrostatic force due to the positive charge. Then which of the following statement is true?

In the figure shown, a conducting sphere of inner radius $a$ and outer radius $b$ is given a charge $Q$. A point charge $q$ is placed in the cavity of this sphere at a distance $x \left(<a\right)$ away from the centre. Find the electric field intensity and electric potential at point $P$ (outside the sphere) at a distance $r \left(>b\right)$. Also, find the electric potential at the point $C$.

Both the ring and the conducting sphere are given the same charge $Q$. Determine the potential of the sphere. Assume that the centre of the sphere lies on the axis of the ring. Is it necessary that the charge on the ring be uniformly distributed to answer the above question?

A solid sphere of the radius $R$ has a cavity of radius $\frac{R}{2}.$ The solid part has a uniform charge density $\rho$ and cavity has no charge. Find the electric potential at the point $A$. Also, find the electric field (only magnitude) at a point $C$ inside the cavity.