A current I flows in a circular arc of radius | vedclass

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(A) The magnetic field at the centre of a complete circular loop carrying current $I$ is given by:$B_{loop} = \frac{\mu_0 I}{2r}$The magnetic field $B

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$\frac{\mu_0 I 	heta}{4 \pi r}$

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(A) The magnetic field at the centre of a complete circular loop carrying current $I$ is given by:$B_{loop} = \frac{\mu_0 I}{2r}$The magnetic field $B$ due to a circular arc of radius $r$ subtending an angle $	heta$ (in radians) at the centre is proportional to the angle subtended by the arc.Since a full circle subtends an angle of $2\pi$ radians,the magnetic field due to an arc subtending an angle $	heta$ is:$B = \left( \frac{	heta}{2\pi} ight) B_{loop}$$B = \left( \frac{	heta}{2\pi} ight) \left( \frac{\mu_0 I}{2r} ight)$$B = \frac{\mu_0 I 	heta}{4 \pi r}$

$A$ current $I$ flows in a circular arc of radius $r$ subtending an angle $\theta$ at the centre $O$ as shown in the figure. Find the magnetic field at the centre $O$ of the circle.

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