Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires.

Question

TestHub · Accepted Answer

Magnitude of magnetic field due to semi-infinite portion of wire AB at point C is

$B_{1} = \frac{μ_{0} i}{4 π r}$

Magnitude of magnetic field due to semicircular arc BD at point C is

$B_{2} = \frac{μ_{0} i}{4 r}$

Magnitude of magnetic field due to semi-infinite portion DE at point C is 0.

Using right-hand rule, it can be seen that directions of $\vec{B_{1}}$ and $\vec{B_{2}}$ are both outwards from the plane.

Therefore, the magnitude of net magnetic field at point C is

$B = B_{1} + B_{2}$

$= \frac{μ_{0} i}{2 r} [\frac{1}{2} + \frac{1}{2 π}]$

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