Question 230: 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: