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Question

The magnetic induction of the field at the point $$O$$ of a loop with current $$I$$, whose shape is illustrated in figure above is given as $$\displaystyle B=\frac{\mu_0}{4\pi}i\left[\frac{x\pi-\varphi}{a}+\frac{\varphi}{b}\right]$$. Find $$x$$ The radii $$a$$ and $$b$$, as well as the angle $$\varphi$$ are known.
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Solution

According to Biot Savart Law, current at the center of circular arc subtending angle $$\theta$$ to the center=$$\dfrac{\mu_0 I}{2 r}\dfrac{\theta}{2\pi}$$
Hence magnetic field at the center of shape shown=$$B=\dfrac{\mu_0 i}{2 a}\dfrac{2\pi-\psi}{2\pi}+\dfrac{\mu_0 i}{2 b}\dfrac{\psi}{2\pi}=\dfrac{\mu_0 i}{4\pi}[\dfrac{2\pi-\psi}{a}+\dfrac{\psi}{b}]$$

Physics
NCERT
Standard XII

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