$A$ circular loop of wire and a long straight wire carry currents $I_c$ and $I_e$,respectively,as shown in the figure. Assuming that these are placed in the same plane,the magnetic field will be zero at the centre of the loop when the separation $H$ is:

$A$ thin ring of $10 \, cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40 \pi \, rad \, s^{-1}$ about its axis,perpendicular to its plane. If the magnetic field at its centre is $3.8 \times 10^{-9} \, T$,then the charge carried by the ring is close to $\left( \mu_0 = 4 \pi \times 10^{-7} \, N/A^2 \right)$.

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. $A$ point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is

The magnetic induction at any point due to a long straight wire carrying a current is

Write the formula for the magnetic field at a point on the axis of a circular current-carrying loop of radius $R$ at a distance $x$ from its center,where $x >> R$.

$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{16}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is [where $\mu_0$ is the permeability of free space].