A current \(I\) a flows in a circular arc of radius \(r\) subtending an angle \(\theta\) as shown in the…

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.

1. \(\frac{\mu_0 I \theta}{4 \pi r}\)
2. \(\frac{2 \mu_0 I \cdot \sin \theta}{4 \pi r}\)
3. \(\frac{2 \mu_0 I \sin \theta}{2 r}\)
4. \(\frac{2 \mu_0 I \sin \theta}{4 r}\)

Solution

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 \(\begin{aligned} & B=\frac{\theta}{2 \pi} \cdot B_C=\frac{\theta}{2 \pi} \cdot \frac{\mu_0 I}{2 r} \text { [From Eq. (i)] } \\ & B=\frac{\mu_0 I \theta}{4 \pi r} \end{aligned}\)

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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