Question 239: Magnetism and Matter

Question

A current $I$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $R.$ The magnitude of the magnetic induction along its axis is:

Accepted Answer

Current in a small element, $dl = {{d	heta } \over \pi }I$
Magnetic field due to the element
$dB = {{{\mu _0}} \over {4\pi }}{{2dl} \over R}$
The component $dB$ $\cos \,	heta ,$ of the field is canceled by another opposite component.
Therefore,
${B_{net}} = \int {dB\sin 	heta  = {{{\mu _0}I} \over {2{\pi ^2}{R_0}}}} $
$\int\limits_0^\pi  {\sin 	heta d	heta  = {{{\mu _0}I} \over {{\pi ^2}R}}} $

Answer

${{{\mu _0}I} \over {2{\pi ^2}R}}$

Answer

${{{\mu _0}I} \over {2\pi R}}$

Answer

${{{\mu _0}I} \over {4\pi R}}$

Answer

${{{\mu _0}I} \over {{\pi ^2}R}}$

Magnetism and Matter

A current I flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius R. The magnitude of the magnetic induction along its axis is:

Choose the correct answer: