NEET Physics Electrostatic Charges and Fields MCQs

A non-conducting sphere of radius $R$ has a volume charge density $\rho = \rho_0(1 - r/R)$, where $\rho_0$ is a constant and $r$ is the distance from the center. The electric field strength at $r = R/2$ is:

A non-conducting spherical shell of inner radius 'a' and outer radius 'b' has a volume charge density $\rho(r) = \frac{A}{r^2}$ for $a \le r \le b$, where A is a constant. A point charge q is placed at the center of the shell. What value of A is required for the electric field to be constant in the region $a < r < b$?

A non-conducting infinitely long solid cylinder of radius 'R' has a uniform volume charge density $\rho$. A spherical cavity of radius 'R/2' is scooped out with its center lying on the axis of the cylinder as shown. If $E_1$ is the magnitude of the electric field at point P (at a distance 'r' from the center of the cavity along the perpendicular bisector of the line joining the center of the cylinder and the center of the cavity where $r > R$) and $E_2$ is the magnitude of the electric field at point Q (at a radial distance 'R/2' from the center of the cavity within the cavity), the ratio $E_1/E_2$ is: