JEE Main 2021 · Physics · Magnetic Effects of Current · medium

A wire carrying current I=10 A forms a closed loop consisting of two concentric semicircular arcs of radii 10 cm and 20 cm in the same plane, joined…

Numerical answer

A wire carrying current

I=10\ \mathrm{A}

forms a closed loop consisting of two concentric semicircular arcs of radii

10\ \mathrm{cm}

and

20\ \mathrm{cm}

in the same plane, joined by straight segments lying along radial lines through the common centre

O

. The current flows clockwise in one arc and anticlockwise in the other. The magnetic field at

O

x\pi\times10^{-7}\ \mathrm{T}

. The value of

x

Show answer and solution

Answer: 50

The straight radial segments contribute nothing at

O

. A semicircular arc gives

B=\dfrac{\mu_0I}{4R}

. Since the current senses are opposite, the fields subtract:

B=\dfrac{\mu_0I}{4}\left(\dfrac1{0.1}-\dfrac1{0.2}\right)=\dfrac{4\pi\times10^{-7}\times10}{4}\times5=50\pi\times10^{-7}\ \mathrm{T}

. So

x=50

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