The magnetic field on the axis of a circular loop of radius 100 ~cm carrying current I= 2 ~A , at point 1 ~m away from the centre of the loop is given by:

Correct answer: A. 3.14 × 10^ -7 ~T As per question, we have; aligned B & =B_0 ^3 θ & = μ_0 I 2 π ^3(45^ ) & = 4 π × 10^ -7 × 2 2 × 1 ( 1 2 )^3 & =3.14 × 10^ -7 ~T aligned

NEET 2022

Exam: NEET
Year: 2022
Subject: Physics
Chapter: Magnetic Effects of Current

NEET 2022 · Physics · Magnetic Effects of Current

The magnetic field on the axis of a circular loop of radius 100 ~cm...

The magnetic field on the axis of a circular loop of radius

100 \mathrm{~cm}

carrying current

I=\sqrt{2} \mathrm{~A}

, at point

1 \mathrm{~m}

away from the centre of the loop is given by:

Options

A $3.14 \times 10^{-7} \mathrm{~T}$
B $6.28 \times 10^{-7} \mathrm{~T}$
C $3.14 \times 10^{-4} \mathrm{~T}$
D $6.28 \times 10^{-4} \mathrm{~T}$

Correct answer

A. $3.14 \times 10^{-7} \mathrm{~T}$

Step-by-step solution

As per question, we have;

\begin{aligned} \mathrm{B} & =\mathrm{B}_0 \sin ^3 \theta \\ & =\frac{\mu_0 \mathrm{I}}{2 \pi} \sin ^3\left(45^{\circ}\right) \\ & =\frac{4 \pi \times 10^{-7} \times \sqrt{2}}{2 \times 1}\left(\frac{1}{\sqrt{2}}\right)^3 \\ & =3.14 \times 10^{-7} \mathrm{~T} \end{aligned}

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