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Q.

A current i amp. flows in the loop having circular arc of r metre subtending an angle $θ$ as shown in fig
The magnetic field at centre O of circle is

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a

$\frac{2 μ_{0}^{i}}{4 {πr}^{2}} \sin θ$

b

$\frac{2 μ_{0} i}{2 r} \sin θ$

c

$\frac{μ_{0} iθ}{4 πr}$

d

$\frac{μ_{0} isin θ}{4 r}$

answer is A.

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Detailed Solution

We know that B $= \frac{μ_{0}}{4 π} \times \frac{2 π \times i}{r}$
Here angle is $θ$ instead of 2 $π$ hence
$B = \frac{μ_{0}}{4 π} \frac{θi}{r}$

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