$A$ steady electric current is flowing through a cylindrical wire. Which of the following statements is/are correct?
$(a)$ The electric field at the axis of the wire is zero.
$(b)$ The magnetic field at the axis of the wire is zero.
$(c)$ The electric field in the vicinity of the wire is zero.
$(d)$ The magnetic field in the vicinity of the wire is zero.

The fractional change in the magnetic field intensity at a distance $r$ from the centre on the axis of a current-carrying coil of radius $a$ to the magnetic field intensity at the centre of the same coil is: (Take $r << a$)

Apply the Biot-Savart law to find the magnetic field due to a circular current-carrying loop at a point on the axis of the loop.

Two concentric circular loops,one of radius $R$ and the other of radius $2R$,lie in the $xy$-plane with the origin as their common center,as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direction and the larger loop carries current $I_2$ in the clockwise direction,with $I_2 > 2I_1$. $\vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $xy$-plane. Which of the following statement$(s)$ is(are) correct?
$(A)$ $\vec{B}(x, y)$ is perpendicular to the $xy$-plane at any point in the plane.
$(B)$ $|\vec{B}(x, y)|$ depends on $x$ and $y$ only through the radial distance $r = \sqrt{x^2 + y^2}$.
$(C)$ $|\vec{B}(x, y)|$ is non-zero at all points for $r$.
$(D)$ $\vec{B}(x, y)$ points normally outward from the $xy$-plane for all the points between the two loops.

Two parallel wires carry currents $i_1$ and $i_2$ $(i_1 > i_2)$. When the currents are in the same direction,the magnetic field at a point midway between the wires is $10 \, \mu T$. When the direction of $i_2$ is reversed,the magnetic field at that point becomes $30 \, \mu T$. What is the ratio $\frac{i_1}{i_2}$?

$A$ 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