Question

Consider a closed loop in the form of a trapezium carrying current $I$. Match the following regarding the magnitude of magnetic field at point $P$.

Answer 1

At P, magnetic field due to AB and CD will be zero.

$\overrightarrow{B_{BC}}=\frac{{\mu }_0}{4\pi }\frac{I}{r}(\sin {\varphi }_1+\sin {\varphi }_2)(-\hat{k})$

$\overrightarrow{B_{DA}}=\frac{{\mu }_0}{4\pi }\frac{I}{3r}(\sin {\varphi }_1+\sin {\varphi }_2)\left(\hat{k}\right)$

$\overrightarrow{B}=\overrightarrow{B_{BC}}+\overrightarrow{B_{DA}}=\frac{2{\mu }_0}{4\pi }\frac{I}{3r}(\sin {\varphi }_1+\sin {\varphi }_2)(-\hat{k})$

$A\to 4$

$B\to 1,2,3$

$C\to 2,3$

$D\to 1,2,3$