The earth’s magnetic field at a given point is $0.5 \times {10^{ - 5}}\,Wb{\rm{ - }}{m^{ - 2}}$. This field is to be annulled by magnetic induction at the center of a circular conducting loop of radius $5.0\,cm$. The current required to be flown in the loop is nearly......$A$

The magnetic field near a current carrying conductor is given by

A tightly wound $100$ turns coil of radius $10 \mathrm{~cm}$ carries a current of $7 \mathrm{~A}$. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4 \pi \times 10^{-7} \mathrm{SI}$ units):

Two concentric coils each of radius equal to $2\pi \,{\rm{ }}cm$ are placed at right angles to each other. $3$ $ampere$ and $4$ $ampere$ are the currents flowing in each coil respectively. The magnetic induction in $Weber/{m^2}$ at the centre of the coils will be $({\mu _0} = 4\pi \times {10^{ - 7}}\,Wb/A.m)$

A current $I$ enters a circular coil of radius $R$, branches into two parts and then recombines as shown in the circuit diagram. The resultant magnetic field at the centre of the coil is

A plastic disc of radius $R$ has a charge $q$ uniformly distributed over its surface. If the disc is rotated at an angular frequency $\omega$ about it axis, the induction at the center of the disc is :-