JEE Physics 2023 Question with Solution

Given: A rectangular loop PQRS is made of uniform wire with $PR = QS = 5 \, \text{cm}$ and $PQ = RS = 100 \, \text{cm}$. The ammeter reading changes from $I$ to $2I$.

Find: The ratio of magnetic force per unit length on wire PQ due to wire RS in the two cases.

The solution states that the magnetic force per unit length varies as the square of current:

$$f \propto I^2$$

Therefore, when current changes from $I$ to $2I$,

$$f_I \propto I^2$$ $$f_{2I} \propto (2I)^2 = 4I^2$$

So,

$$f_I : f_{2I} = 1 : 4$$

the solution concludes that the correct option is D. However, among the given options, $1:4$ is listed as option B. Hence the worked result supports $1:4$, and the matching option is B.

The provided solution text derives

$$f_I : f_{2I} = 1 : 4$$

but the solution says The Correct Option is D. Since option D in the listed options is $1:3$, this conflicts with the actual derivation shown in the solution. Following the working, the defensible answer is B corresponding to $1:4$.