JEE Physics 2026 Question with Solution

Given: Two identical circular loops $P$ and $Q$ have radius $r$. Currents are $I$ and $4I$ respectively. Point $O$ lies on the common axis, at distance $r$ from each loop.

Find: The net magnetic field at $O$ and its direction.

Magnetic field on the axis of a circular loop is

$$B = \frac{\mu_0 I r^2}{2(r^2 + x^2)^{3/2}}$$

where $x$ is the distance of the point from the centre of the loop.

For loop $P$, current is $I$ and $x = r$. Therefore,

$$B_P = \frac{\mu_0 I r^2}{2(r^2 + r^2)^{3/2}} = \frac{\mu_0 I r^2}{2(2r^2)^{3/2}} = \frac{\mu_0 I}{4\sqrt{2}r}$$

Using the right-hand thumb rule, its direction is towards $P$.

For loop $Q$, current is $4I$ and $x = r$. Therefore,

$$B_Q = \frac{\mu_0 (4I) r^2}{2(r^2 + r^2)^{3/2}} = \frac{4\mu_0 I r^2}{2(2r^2)^{3/2}} = \frac{\mu_0 I}{\sqrt{2}r}$$

Its direction is towards $Q$.

The two magnetic fields are opposite in direction, so the net magnitude is

$$B_{\text{net}} = B_Q - B_P = \frac{\mu_0 I}{\sqrt{2}r} - \frac{\mu_0 I}{4\sqrt{2}r} = \frac{3\mu_0 I}{4\sqrt{2}r}$$

The solution states the direction of the net field is towards $P$.

Therefore, the correct option is C.

Given: Both loops carry clockwise current as seen from $O$.

Find: Which field dominates at $O$.

First determine the direction of the field due to each loop using the right-hand thumb rule. At point $O$, the field due to loop $P$ is towards $P$, while the field due to loop $Q$ is towards $Q$. Hence the two fields oppose each other.

Now compare magnitudes using

$$B \propto \frac{I r^2}{(r^2 + x^2)^{3/2}}$$

Since both loops have the same radius and the point $O$ is at the same distance $r$ from each centre, the denominator is identical for both loops. Therefore, magnitudes are in the ratio of currents:

$$B_P : B_Q = I : 4I = 1 : 4$$

So the field due to loop $Q$ is larger. The net field must therefore be in the direction associated with the larger field, as stated in the solution, giving magnitude

$$\frac{3\mu_0 I}{4\sqrt{2}r}$$

and direction towards $P$.

Therefore, the correct option is C.