$A$ long straight wire carrying a current of $30\,A$ is placed in an external uniform magnetic field of induction $4 \times 10^{-4}\,T$. The magnetic field is acting parallel to the direction of the current. The magnitude of the resultant magnetic induction in tesla at a point $2.0\,cm$ away from the wire is

$A$ circular coil of radius $R$ carries an electric current $I$. The magnetic field due to the coil at a point on the axis of the coil located at a distance $r$ from the centre of the coil,such that $r \gg R$,the magnetic field at that point is proportional to

Two infinite length wires are placed as shown in the figure. Find the magnitude of the magnetic field at point $M$,which is the midpoint of the line joining the two wires.

$A$ circular current-carrying coil has radius $R$. At what distance from the centre of the coil on the axis,the magnetic induction will become $\frac{1}{8}$ th of its value at the centre of the coil?

$A$ beam of neutrons performs circular motion of radius $r = 1 \, m$ under the influence of an inhomogeneous magnetic field with inhomogeneity extending over $\Delta r = 0.01 \, m$. The speed of the neutrons is $54 \, m/s$. The mass and magnetic moment of the neutrons are $1.67 \times 10^{-27} \, kg$ and $9.67 \times 10^{-27} \, J/T$ respectively. The average variation of the magnetic field over $\Delta r$ is approximately ....... $T$.

Current $I$ is flowing in a conductor shaped as shown in the figure. The radius of the curved part is $r$ and the length of the straight portions is very large. The value of the magnetic field at the centre $O$ will be