In the above figure,the magnetic field at poi | vedclass

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Question

(A) The magnetic field at point $C$ is the vector sum of the fields produced by the three segments of the wire: two semi-infinite straight wires and o

Vedclass · Accepted Answer

$\frac{{\mu _0}i}{{4\pi r}}\left[ {\left( {1 + \pi } \right)\hat k - \hat i} \right]$

Vedclass · Answer

(A) The magnetic field at point $C$ is the vector sum of the fields produced by the three segments of the wire: two semi-infinite straight wires and one semi-circular arc.$1$. For the semi-infinite straight wire along the $x$-axis (carrying current towards the origin),the field at $C$ (at distance $r$) is given by $B_1 = \frac{\mu_0 i}{4\pi r} (-\hat{i})$.$2$. For the semi-circular arc of radius $r$,the field at the center is $B_2 = \frac{\mu_0 i}{4r} \hat{k}$.$3$. For the semi-infinite straight wire starting from the origin (carrying current away from the origin),the field at $C$ is $B_3 = \frac{\mu_0 i}{4\pi r} \hat{k}$.Summing these: $\vec{B}_C = B_1 + B_2 + B_3 = \frac{\mu_0 i}{4\pi r} (-\hat{i}) + \frac{\mu_0 i}{4r} \hat{k} + \frac{\mu_0 i}{4\pi r} \hat{k}$.Factoring out $\frac{\mu_0 i}{4\pi r}$,we get: $\vec{B}_C = \frac{\mu_0 i}{4\pi r} [ (1 + \pi) \hat{k} - \hat{i} ]$.

In the above figure,the magnetic field at point $C$ will be:

Similar Questions

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