Question

Earth’s magnetic field at magnetic equator is approximately $0.4G$. Earth’s dipole moment is ($r_e=6400km$)

• A. $4\times {10}^{-5}T$
• B. $4\times {10}^{2}T$
• C. $1.05\times {10}^{23}T$
• D. $1.05\times {10}^{-20}T$

Answer 1

The correct option is C

$1.05\times {10}^{23}T$

Step 1: Given data

Earth's magnetic field, $B=0.4G=0.4\times {10}^{-4}T$

Radius of earth, $r_e=6400km$

Step 2: Formula used

Magnetic field is given by $B=\frac{\mu M}{4\pi {r_e}^3}$(Assuming earth to behave like a bar magnet)

$\mu$=Absolute magnetic permeability of free space

$M$=Earth's dipole moment

Step 3: Calculation of dipole moment

We have, $\frac{\mu }{4\pi }={10}^{-7}Wb{A}^{-1}{m}^{-1}$

We get, $M=\frac{B{r^3}_e}{{10}^{-7}}=\frac{0.4\times {10}^{-4}\times {\left(6400\times 1000\right)}^3}{{10}^{-7}}$

$M=1.05\times {10}^{23}A{m}^2$

Hence, option (C) is the correct answer.