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  • Find the magnetic induction of the field at the point O of a loop with current i, whose shape is illustrated. A current i

Find the magnetic induction of the field at the point O of a loop with current i, whose shape is illustrated. A current i flows along a thin wire shaped as shown in figure. The radius of a curved part of a wire is canal to R, the angle is 2 \phi. Find the magnetic induction of the field at the Point O .

Option: 1

B=(\pi-\phi+\sin \phi) \mu_0 \frac{1}{2 \pi R}


Option: 2

B=(\pi-\phi+\tan \phi) \mu_0 \frac{1}{2 R}


Option: 3

B=(\pi-\phi+\tan \phi) \mu_0 \frac{1}{ R}


Option: 4

None


Answers (1)

Magnetic field due to Arc_1 B_1 =\frac{\mu_0 i}{4 \pi R}(2 \pi-2 \phi) \\

B_1=\frac{\mu_0 i}{2 \pi R}(\pi-\phi)

Magnetic field due to straight wire,

B_2=\frac{\mu_0 i}{4 \pi R \cos \phi} \times 2 \sin \phi

B_2=\frac{\mu_{0 i}}{2 \pi R} \tan \phi \\

\therefore B_{\text {net }}=B_1+B_2=\frac{\mu_{0 i}}{2 \pi R}[\pi-\phi+\tan \phi]

Posted by

Sumit Saini

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