Question

If the radius of the Earth is \( 6.4 \times 10^6 \, m \) and its magnetic dipole moment is \( 1.3 \times 10^{23} \, Am^2 \), then the magnetic field at the equator is:

• A. 0.5 G
• B. 0.3 G
• C. 0.7 G
• D. 0.35 G

Hint:

The magnetic field due to a magnetic dipole moment is given by \( B = \frac{\mu}{4 \pi R^3} \), where \( R \) is the distance from the dipole.

Answer 1

The Correct Option is A

The magnetic field at the equator due to Earth's magnetic dipole moment is given by: \[ B = \frac{\mu}{4 \pi R^3} \] Substituting the given values: \[ B = \frac{1.3 \times 10^{23}}{4 \pi (6.4 \times 10^6)^3} \] After performing the calculation: \[ B \approx 0.5 \, \text{G} \] Thus, the magnetic field at the equator is \( 0.5 \, \text{G} \).