List of top Electromagnetic Fields Questions asked in GATE EE

In the figure, the electric field \(E\) and the magnetic field \(B\) point to \(z\) and \(x\) directions, respectively, and have constant magnitudes. A positive charge \(q\) is released from rest at the origin. Which of the following statement(s) is/are true? \begin{center} \includegraphics[width=0.45\textwidth]{20.jpeg} \end{center}
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
If the magnetic field intensity \( H \) in a conducting region is given by the expression, \[ H = x^2 \hat{i} + x^2 y^2 \hat{j} + x^2 y^2 z^2 \hat{k} \, \text{A/m.} \] The magnitude of the current density, in A/m\(^2\), at \( x = 1 \, m \), \( y = 2 \, m \), and \( z = 1 \, m \), is
A long conducting cylinder having a radius ‘b’ is placed along the z axis. The current density is \( J = J_a r^3 \hat{z} \) for the region \( r<b \) where \( r \) is the distance in the radial direction. The magnetic field intensity (H) for the region inside the conductor (i.e. for \( r<b \)) is

Which one of the following vector functions represents a magnetic field $\vec{B}$?   ($\hat{x}$, $\hat{y}$, and $\hat{z}$ are unit vectors along x-axis, y-axis, and z-axis, respectively)

A parallel-plate capacitor with dielectric of relative permittivity 5 is charged to \(V\) and disconnected. The slab is pulled out completely. The ratio of new electric field \(E_2\) to original field \(E_1\) is \(\underline{\hspace{2cm}}\).
One coulomb of point charge moving with a uniform velocity \(10\hat{x}\) m/s enters the region \(x \ge 0\) having magnetic flux density \(\vec{B} = (10y\hat{x} + 10x\hat{y} + 10\hat{z})\) T. The magnitude of force on the charge at \(x = 0^+\) is \(\underline{\hspace{2cm}}\) N.
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 \[ \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9} \]