List of top Electromagnetic Fields Questions

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}

Given below are two statements:
Statement-I: The tangential component of the electric field intensity is continuous across an interface between two general materials, regardless of charge densities on the surface.
Statement-II The tangential component of the electric flux density is discontinuous across the interface. The discontinuity is equal to the ratio between the permittivities of the materials. 
In the light of the above statements, choose the correct answer from the options given below.

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