Concepts Of Physics MCQ Edition [Volume 2]PhysicsPermanent Magnets
Assume the magnetic moment of the dipole at the earth's centre is 8.0 10²² A m ^2 . Determine the magnetic field B at the earth's geomagnetic poles. The radius of the earth is 6400 km .
Options
- A3.1 10⁻⁵ T
- B6.1 10⁻⁵ T
- C1.2 10⁻⁴ T
- D6.1 10⁻⁴ T
Correct answer
B. 6.1 10⁻⁵ T
Step-by-step solution
The magnetic field at the geomagnetic poles (which lie on the axial line of the earth's magnetic dipole) is given by: B = ₀ 4 2M R^3 Given: M = 8.0 10²² A m ^2 R = 6400 km = 6.4 10^6 m ₀ 4 = 10⁻⁷ T m A ⁻¹ Substituting the values: B = 10⁻⁷ 2 8.0 10²² (6.4 10^6)^3 B = 10⁻⁷ 16.0 10²² 262.144 10¹⁸ B = 10⁻⁷ 0.061 10^4 B = 6.1 10⁻⁵ T