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A current \(I\) a flows in a circular arc of radius \(r\) subtending an angle \(\theta\) as shown in the figure. Find the magnetic field at the centre \(O\) of the circle.
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Verified Answer
The correct answer is:
\(\frac{\mu_0 I \theta}{4 \pi r}\)
Magnetic field at the centre due to current carrying circular loop is given as
\(B_C=\frac{\mu_0 I}{2 r}\) ...(i)
Magnetic field due to current carrying circular arc making an angle \(\theta\) at the centre, is given as
\(\begin{aligned}
& B=\frac{\theta}{2 \pi} \cdot B_C=\frac{\theta}{2 \pi} \cdot \frac{\mu_0 I}{2 r} \text { [From Eq. (i)] } \\
& B=\frac{\mu_0 I \theta}{4 \pi r}
\end{aligned}\)
\(B_C=\frac{\mu_0 I}{2 r}\) ...(i)
Magnetic field due to current carrying circular arc making an angle \(\theta\) at the centre, is given as
\(\begin{aligned}
& B=\frac{\theta}{2 \pi} \cdot B_C=\frac{\theta}{2 \pi} \cdot \frac{\mu_0 I}{2 r} \text { [From Eq. (i)] } \\
& B=\frac{\mu_0 I \theta}{4 \pi r}
\end{aligned}\)
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