Two circular coils $P$ and $Q$ are made from similar wire,but the radius of $Q$ is twice that of $P$. What should be the value of the potential difference across them so that the magnetic induction at their centres is the same?

$A$ long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $n$ turns. If the same current is passed in both the cases, the ratio of magnetic field produced at the centre for one turn to that of $n$ turns is

Write the equation for the magnetic field of a current-carrying circular loop at: $(i)$ a point on the axis,and $(ii)$ a point on the plane of the loop at a distance $x$ from the center of the loop.

$A$ non-conducting thin disc of radius $R$ rotates about its axis with an angular velocity $\omega$. The surface charge density on the disc varies with the distance $r$ from the center as $\sigma(r)=\sigma_0\left[1+\left(\frac{r}{R}\right)^\beta\right]$, where $\sigma_0$ and $\beta$ are constants. If the magnetic induction at the center is $B=\left(\frac{9}{10}\right) \mu_0 \sigma_0 \omega R$, the value of $\beta$ is

Which of the following graphs correctly represents the variation of magnetic field $B$ with distance $R$ from a long straight current-carrying conductor?

$A$ current carrying circular coil of radius $R$ produces magnetic fields $B_1$ and $B_2$ at an axial point $P$ at a distance $x$ from its centre and at a point $Q$ placed at its centre respectively. If $B_1 = \frac{B_2}{8}$,the value of $x$ is