List of top Electromagnetic Fields Questions on Electric field and potential due to point asked in GATE EE

A uniform spherical volume charge distribution of radius \(2\) m, centered at the origin, has a strength of \(\frac{3}{\pi}\times10^{-6}\) C/m\(^3\). A point charge of strength \(\pi\times8.854\times10^{-12}\) C is moved from \((-3,0,-4)\) to \((0,0,4)\) in Cartesian coordinate system. The relative permittivity of the medium is \(1\) and the coordinate values are in meters.
The work done during the process is \(\mu\)J (round off to two decimal places).

As shown in the figure below, two concentric conducting spherical shells, centered at \( r = 0 \) and having radii \( r = c \) and \( r = d \) are maintained at potentials such that the potential \( V(r) \) at \( r = c \) is \( V_1 \) and \( V(r) \) at \( r = d \) is \( V_2 \). Assume that \( V(r) \) depends only on \( r \), where \( r \) is the radial distance. The expression for \( V(r) \) in the region between \( r = c \) and \( r = d \) is

A 1 µC point charge is held at the origin. A second point charge of 10 µC is moved from (0,10,0) to (5,5,5) and then to (5,0,0). The total work done is \(\underline{\hspace{2cm}}\) mJ. (Round off to 2 decimal places).
Take \[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9} \]