A circular arc of radius r carrying current I | vedclass

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(C) The magnetic field $B$ at the centre of a circular arc of radius $r$ carrying current $I$ that subtends an angle $	heta$ at the centre is given b

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$\frac{\mu_{0} I}{64 r}$

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(C) The magnetic field $B$ at the centre of a circular arc of radius $r$ carrying current $I$ that subtends an angle $	heta$ at the centre is given by the formula:$B = \frac{\mu_{0} I 	heta}{4 \pi r}$Here,the angle subtended is $	heta = \frac{\pi}{16}$.Substituting the value of $	heta$ into the formula:$B = \frac{\mu_{0} I}{4 \pi r} 	imes \left( \frac{\pi}{16} ight)$$B = \frac{\mu_{0} I \pi}{64 \pi r}$$B = \frac{\mu_{0} I}{64 r}$Thus,the correct option is $C$.

$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{16}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is

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