JEE Physics 2023 Question with Solution

Given: Four current configurations in List I are to be matched with the magnetic field expressions at point $O$ in List II.

Find: The correct matching between configurations $A, B, C, D$ and expressions $I, II, III, IV$.

Using Biot-Savart law for each configuration:

1. For configuration $A$,

So $A \to III$.

2. For configuration $B$,

This corresponds to expression $I$. So $B \to I$.

3. For configuration $C$,

This corresponds to expression $IV$. So $C \to IV$.

4. For configuration $D$,

This corresponds to expression $II$. So $D \to II$.

Thus, the correct match is A-III, B-I, C-IV, D-II.

Therefore, the correct option is C.

Given: The magnetic field at point $O$ must be identified for each wire configuration.

Find: Which option gives the correct one-to-one correspondence.

The solution states the following results directly:

• Configuration $A$ gives $\dfrac{\mu_0 I}{4\pi r}[\pi + 2]$
• Configuration $B$ gives $\dfrac{\mu_0 I}{4\pi r}[2\pi - 1]$
• Configuration $C$ gives $\dfrac{\mu_0 I}{4\pi r}[\pi - 1]$
• Configuration $D$ gives $\dfrac{\mu_0 I}{4\pi r}[2\pi + 1]$

Now compare these with the expressions shown in List II of the figure. This gives:

• $A \to III$
• $B \to I$
• $C \to IV$
• $D \to II$

Hence the only matching option is A-III, B-I, C-IV, D-II.

Therefore, the correct option is C.