Electromagnetic Induction and Maxwell Equations - Electricity and Magnetism - Instrumentation Engineering Previous Year Questions

A vector is defined as
\(\mathbf{f} = y\hat{i} + x\hat{j} + z\hat{k}\)
where \(\hat{i}, \hat{j}\) and \(\hat{k}\) are unit vectors in Cartesian \((x,y,z)\) coordinate system.
The surface integral \(\oint \mathbf{f} \cdot d\mathbf{s}\) over the closed surface \(S\) of a cube with vertices having the following coordinates: \((0,0,0), (1,0,0), (1,1,0), (0,1,0), (0,0,1), (1,0,1), (1,1,1), (0,1,1)\) is ________.

A beam of monochromatic light passes through two glass slabs of the same geometrical thickness at normal incidence. The refractive index of the first slab is 1.5 and that of the second, 2.0. The ratio of the time of passage of the beam through the first to the second slab is ______ .

A 60 V DC source with an internal resistance \(R_{int}=0.5\Omega\) is connected through a switch to a pair of infinitely long rails separated by \(l=1\)m as shown in the figure. The rails are placed in a constant, uniform magnetic field of flux density \(B=0.5\)T, directed into the page. A conducting bar placed on these rails is free to move. At the instant of closing the switch, the force induced on the bar is
Note: Assume there is no friction between the bar and the rails. The resistances of the conducting bar and the rails are zero.

The vector function \(\vec{A}\) is given by \(\vec{A} = \nabla u\), where \(u(x,y)\) is a scalar function. Then \(|\nabla \times \vec{A}|\) is

As shown in the figure, a slab of finite thickness t with refractive index n₂ = 1.5, has air (n₁ = 1) above and below it. Light of free space wavelength 600 nm is incident normally from air as shown. For a destructive interference to be observed at R, the minimum value of thickness of the slab t (in nm) is ____

A conducting semi-circular loop of radius \(R = 0.1\) m, with its diameter centered at the origin, rotates in the \(x-y\) plane about the origin with a constant angular velocity, \(\omega = 20\) rad/s, as shown. A magnetic field of magnitude \(B = 2\) T and normal to \(x-y\) 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)

Inductance of a coil is measured as 10 mH, using an LCR meter, when no other objects are present near the coil. The LCR meter uses a sinusoidal excitation at 10 kHz. If a pure copper sheet is brought near the coil, the same LCR meter will read__________.