The magnetic field at the centre of a current carrying circular loop of radius \(R\) is 16 \(\mu\)T. The magnetic field at a distance \(x = \sqrt{3}R\) on its axis from the centre is ________ \(\mu\)T.

Choose the correct option:

A wire carrying current \(I\) is bent in the shape \(A\,B\,C\,D\,E\,F\,A\) as shown, where rectangle \(A\,B\,C\,D\,A\) and \(A\,D\,E\,F\,A\) are perpendicular to each other. If the sides of the rectangles are of lengths \(a\) and \(b,\) then the magnitude and direction of magnetic moment of the loop \(A\,B\,C\,D\,E\,F\,A\,\) is

All resistances in figure are \(1\,\Omega\) each. The value of current ' \(I\) ' is \(\frac{a}{5}\,A\). The value of \(a\) is

A copper wire is wound on a wooden frame, whose shape is that of an equilateral triangle. If the linear dimension of each side of the frame is increased by a factor of \(3\), keeping the number of turns of the coil per unit length of the frame the same, then self inductance of the coil

The velocity of a particle executing SHM varies with displacement \(( x )\) as \(4 v ^2=50- x ^2\). The time period of oscillations is \(\frac{x}{7} s\). The value of \(x\) is \(............\) \(\left(\right.\) Take \(\left.\pi=\frac{22}{7}\right)\)

An electron revolving in \(\mathrm{n}^{\text {th }}\) Bohr orbit has magnetic moment \(\mu_n\). If \(\mu_n\) \(\alpha\) \(n^x\), the value of \(x\) is _______.

Consider a spherical shell of radius \(R\) at temperature \(T\). The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume\(E=\) \(\frac{U}{V} \propto {T^4}\) and pressure \(P = \frac{1}{3}\left( {\frac{U}{V}} \right)\) If the shell now undergoes an adiabatic expansion the relation between \(T\) and \(R\) is

The equivalent capacitance between points \(A\) and \(B\) in below shown figure will be..........\(\mu F\).