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JEE Main 201325 AprilOnline

Exam: JEE Main
Year: 2013
Date: 25 April
Mode: Online
Subject: Physics
Chapter: Magnetic Properties of Matter

JEE Main 2013 · 25 April · Online · Physics · Magnetic Properties of Matter

The earth's magnetic field lines resemble that of a dipole at the...

The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to

8 \times 10^{22} \mathrm{Am}^2

, the value of earth's magnetic field near the equator is close to (radius of the earth

\left.=6.4 \times 10^6 \mathrm{~m}\right)

Options

A $0.6$ Gauss
B $1.2$ Gauss
C $1.8$ Gauss
D $0.32$ Gauss

Correct answer

A. $0.6$ Gauss

Step-by-step solution

Given

M=8 \times 10^{22} \mathrm{Am}^2

\mathrm{d}=\mathrm{R}

_{\mathrm{e}}=

6.4

\times

10^6

\mathrm{~m}

Earth's magnetic field,

\mathrm{B}=\frac{\mu_0}{4 \pi} \cdot \frac{2 \mathrm{M}}{\mathrm{d}^3}

\begin{aligned}&=\frac{4 \pi \times 10^{-7}}{4 \pi} \times \frac{2 \times 8 \times 10^{22}}{\left(6.4 \times 10^6\right)^3}\\ &\cong 0.6 \text{ Gauss } \end{aligned}

$$

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