List of top Electricity and Magnetism Questions asked in GATE IN

A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air = \(8.854 \times 10^{-12} \, \text{F/m}\)). The radii of the inner and outer spheres are \(a = 10 \, \text{cm}\) and \(b = 15 \, \text{cm}\), respectively. The capacitance (in picofarads) is _________ (round off to 2 decimal places).
A conducting semi-circular loop of radius \( R = 0.1 \, \text{m} \), with its diameter centered at the origin, rotates in the \( x \)-\( y \) plane about the origin with a constant angular velocity, \( \omega = 20 \, \text{rad/s} \), as shown. A magnetic field of magnitude \( B = 2 \, \text{T} \) and normal to the \( x \)-\( y \) plane exists in the region \( x \geq 0 \) as shown. If the loop has a resistance of \( 2 \, \Omega \), and negligible inductance, the peak-to-peak current (in milliamperes) in the loop is _________ (round off to one decimal place)

The figure below shows an electrically conductive bar of square cross-section resting on a plane surface. The bar of mass of 1 kg has a depth of 0.5 m along the y direction. The coefficient of friction between the bar and the surface is 0.1. Assume the acceleration due to gravity to be 10 m/s\(^2\). The system faces a uniform flux density \( B = -1 \hat{z} \, \text{T} \). At time \( t = 0 \), a current of 10 A is switched onto the bar and is maintained. When the bar has moved by 1 m, its speed in metre per second is \(\underline{\hspace{2cm}}\) (rounded off to one decimal place). 
 

A toroid made of CRGO has an inner diameter of 10 cm and an outer diameter of 14 cm. The thickness of the toroid is 2 cm. 200 turns of copper wire is wound on the core. \( \mu_0 = 4\pi \times 10^{-7} \, \text{H/m} \) and \( \mu_r \) of CRGO is 3000. When a current of 5 mA flows through the winding, the flux density in the core in millitesla is \(\underline{\hspace{2cm}}\).
An infinitely long line, with uniform positive charge density, lies along the z-axis. In cylindrical coordinates \( (r, \phi, z) \), at any point \( \mathbf{P} \) not on the z-axis, the direction of the electric field is