List of top Physics Questions on Electromagnetism asked in GATE PH

A capacitor is made of two circular metal plates of radius 1 m, separated by a distance \(d = 1\text{ mm}\). The space between the plates is filled with a dielectric of permittivity \(\epsilon_r = 5\). The capacitor is connected to a voltage \(V = 10\sin(2\pi \times 10^6 \times t)\) volts, where \(t\) is in seconds. The maximum value of the magnetic field between the plates, at a radial distance \(r = 0.5\text{ m}\) from the centre, is \(B \times 10^{-6}\text{ T}\). The value of \(B\) (rounded off to two decimal places) is ______.
(Speed of light in vacuum \(c = 3 \times 10^8\text{ m.s}^{-1}\))

An infinitely large thin sheet in the \(xy\)-plane carries uniform positive charge density and is moving with constant velocity \(\vec{v}\) in the \(+x\) direction (see figure below). The direction of the corresponding Poynting vector is

A positive point charge is fixed at the origin. At some distance from it on the \(x\) axis, a point dipole is kept pointing in the \(+y\) direction. The force on the dipole is

For the electric field of an electromagnetic wave given below, which of the following statements is correct?
\[ \vec{E} = \hat{x}\, E_0 \cos(\omega t) + \hat{y}\, 2E_0 \cos\left(\omega t + \frac{\pi}{2}\right) \]

An infinitely large non-conducting thin sheet in the \(xy\) plane (\(z=0\)) carries a uniform surface charge density \(\sigma = 17.70\times10^{-12}\) C.m\(^{-2}\). The electric field in the region \(z < 0\) is \(\vec{E}_2 = \hat{x}+2\hat{y}+3\hat{z}\). Then, the electric field \(\vec{E}_1\) in the region \(z > 0\) will be (\(\epsilon_0 = 8.85\times10^{-12}\) C\(^2\).N\(^{-1}\).m\(^{-2}\))

Which of the following options is correct for transformation of electric field \(\vec{E}\) and magnetic field \(\vec{B}\) under time reversal, i.e., \(t \to -t\)?

In free space, an electromagnetic wave is travelling whose wavevector is \(\vec{k} = 10(\hat{x} + \sqrt{3}\hat{y})\) m\(^{-1}\). The electric field component of this electromagnetic wave is given by \(\vec{E}(\vec{r},t) = \hat{z}\, 600\cos(\vec{k}\cdot\vec{r} - \omega t)\) V.m\(^{-1}\). The speed of light in free space is \(c = 3.0 \times 10^{8}\) m.s\(^{-1}\). The corresponding magnetic field \(\vec{B}(\vec{r},t)\) is