JEE Advanced Physics Question (2022) — Solution

Step-by-step solution

Magnetic field due to a straight wire will be zero if the line of the wire passes through the point of interest. Therefore, In the above figure, B B C + B D E + B F G = 0 Therefore, B → net   = B → A B + B → C D   + B → E F Magnetic field due to a finite wire is given by, B = μ 0 I 4 π d sin α + sin β Using above formula, B → A B = μ 0 I 4 π L × 1 2 - k ^ Magnetic field due to a circular arc is, B = μ 0 I 2 R × θ 2 π Therefore, B → C D = μ 0 I 4 L 2 - k ^  and  B → E F = μ 0 I 8 × L 4 - k ^ Therefore, net magnetic field B → net = μ 0 I 4 π × L 1 2 + μ 0 I 4 L 2 + μ 0 I 8 × L 4 - k ^ ⇒ B → net = μ 0 I 2 L + μ 0 I 2 L + μ 0 I 4 2 π L - k ^ ⇒ B → net = μ 0 I L 1 + 1 4 2 π - k ^