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JEE Main 202226 JulyMorning Shift

Exam: JEE Main
Year: 2022
Date: 26 July
Shift: Morning Shift
Subject: Physics
Chapter: Magnetic Effects of Current

JEE Main 2022 · 26 July · Morning Shift · Physics · Magnetic Effects of Current

B _ X and B _ Y are the magnetic field at the centre of two coils...

{B}_{X}

and

{B}_{Y}

are the magnetic field at the centre of two coils of two coils

X

and

Y

respectively, each carrying equal current. If coil

X

has

200

turns and

20cm

radius and coil

Y

has

400

turns and

20cm

radius, the ratio of

{B}_{X}

and

{B}_{Y}

is

Options

A $1: 1$
B $1: 2$
C $2: 1$
D $4: 1$

Correct answer

B. $1: 2$

Step-by-step solution

Magnetic field at the centre of a single coil is $B = \dfrac{{\mu}_{0}i}{2R}$
If $N$ number of loops are kept closely $B = N\left(\dfrac{{\mu}_{0}i}{2R}\right)$
Therefore,
$\dfrac{{B}_{x}}{{B}_{y}} = \dfrac{{N}_{x}}{{N}_{y}}$
$⇒ \dfrac{{B}_{x}}{{B}_{y}} = \dfrac{1}{2}$

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