Exam

JEE Main

Year

2014

Date

9 April

Mode

Online

Subject

Physics

Chapter

Magnetic Properties of Matter

JEE Main 2014 · 9 April · Online · Physics · Magnetic Properties of Matter

The magnetic field of earth at the equator is approximately 4 × 1 0...

The magnetic field of earth at the equator is approximately $4 \times 1 {0}^{- 5} \text{T}$. The radius of earth is $\text{6.4} \times 1 {0}^{6} \text{m}$. Then the dipole moment of the earth will be nearly of the order of :

Step-by-step solution

$\text{B} = \dfrac{{\mu}_{0}}{4 \pi} \cdot \dfrac{\text{M}}{{\text{d}}^{3}} = 1 {0}^{- 7} \times \dfrac{\text{M}}{{\left(\text{6.4} \times 1 {0}^{6}\right)}^{3}}$

$∴ 4 \times 1 {0}^{- 5} = \dfrac{1 {0}^{- 7} \times \text{M}}{{\left(\text{6.4} \times 1 {0}^{6}\right)}^{3}}$

$∴ \text{M} = \dfrac{{\left(\text{6.4} \times 1 {0}^{6}\right)}^{3} \times 4 \times 1 {0}^{- 5}}{1 {0}^{- 7}}$

$= {\left(\text{6.4}\right)}^{3} \times 1 {0}^{1 8} \times 4 \times 1 {0}^{2}$

$= {\left(\text{6.4}\right)}^{3} \times 4 \times 1 {0}^{2 0}$

$= 1 \text{.} 0 4 8 \times 1 {0}^{2 3}$ $\approx {10}^{23} A{m}^{2}$