JEE Main 2018 · Physics · Magnetic Effects of Current · medium

A closed circuit consists of two coplanar semicircular arcs of radii 10 cm and 20 cm with a common centre O, joined at their ends by straight wires…

Single correct option

A closed circuit consists of two coplanar semicircular arcs of radii

10\ \mathrm{cm}

and

20\ \mathrm{cm}

with a common centre

O

, joined at their ends by straight wires lying along the line through

O

. A current of

5\ \mathrm{A}

flows round the circuit. The magnitude of the magnetic field at

O

is nearly

Show answer and solution

Answer: (D) $7.85\ \mu\mathrm{T}$

The straight segments are collinear with

O

, so they contribute nothing. A semicircular arc of radius

a

gives

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

. Going once round the closed circuit, the current runs counter-clockwise on one arc and clockwise on the other, so their fields at

O

are opposite:

B=\dfrac{\mu_0I}{4}\left(\dfrac1{0.1}-\dfrac1{0.2}\right)=10^{-7}\pi\times5\times5=7.85\times10^{-6}\ \mathrm{T}

. Adding the two contributions, which would be wrong here, gives

23.6\ \mu\mathrm{T}

Original question written in the JEE Main 2018 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake