Question

Time varying magnetic field is present in a circular region of radius $R$. Match the properties from column-2 to column-1 using the codes given below the columns.

Column-I	Column-II
(P) An unsteady magnetic field	(1) Electric field is perpendicular to the length of rod.
(Q) Induced electric field at a point within magnetic field ($r<R$)	(2) $\frac{r}{2}\frac{dB}{dt}$
(R) Induced electric field at a point outside the magnetic field ($r>R$)	(3) $\frac{R^2}{2r}\frac{dB}{dt}$
(S) If a rod is placed along the diameter of the magnetic field	(4) Induced electric field

• A. P - 4, Q - 2, R - 1, S - 1
• B. P - 1, Q - 1, R - 3, S - 4
• C. P - 1, Q - 4, R - 1, S - 4
• D. P - 4, Q - 2, R - 3, S - 1

Answer 1

The correct option is D P - 4, Q - 2, R - 3, S - 1

When an electrically-conducting structure is exposed to a time-varying magnetic field, an electrical potential difference is induced across the structure. This phenomenon is known as electromagnetic induction.



So, (P) $\to$ (4)

For $r<R$,
$\$\oint E.dl=-A\frac{dB}{dt}E.2\pi r=-\pi r^2\frac{dB}{dt}E=-\frac{r}{2}\frac{dB}{d\mathrm{t\$}}$
So, (Q) $\to$ (2)

For $r>R$
$E.2\pi r=-\pi R^2\frac{dB}{dt}$
$\Rightarrow E=-\frac{R^2}{2r}\frac{dB}{dt}$
Hence, (R) $\to$ (3)

If rod is placed along the diameter of the magnetic field, then electric field is perpendicular to the length of rod ( Fleming right hand rule).
Hence, (S) $\to$ (1)