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A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is:
Detailed Solution
For an arc, $B=\frac{\mu_0 i\theta}{4\pi R}$. The two arcs (270° and 90°) are in parallel, so $\frac{i_1}{i_2}=\frac{R_2}{R_1}=\frac{l_2}{l_1}=\frac{\theta_2}{\theta_1}$, giving $i_1\theta_1=i_2\theta_2$. The fields are equal in magnitude and opposite in direction, so the net field at P is zero.