Concepts Of Physics MCQ Edition [Volume 2]PhysicsPermanent Magnets
Suppose the magnitude of the earth's magnetic field at the magnetic equator is 3.4 10⁻⁵ T . Find its value at the geomagnetic poles of the earth.
Options
- A4.8 10⁻⁵ T
- B3.4 10⁻⁵ T
- C6.8 10⁻⁵ T
- D1.7 10⁻⁵ T
Correct answer
C. 6.8 10⁻⁵ T
Step-by-step solution
The earth's magnetic field can be approximated as a magnetic dipole. The magnitude of the magnetic field of a short dipole at a distance r and magnetic latitude is given by: B = ₀ M 4 r^3 1 + 3 ^2 At the magnetic equator, = 0^ , so = 0 . B_ eq = ₀ M 4 r^3 = 3.4 10⁻⁵ T At the geomagnetic poles, = 90^ , so = 1 . B_ pole = ₀ M 4 r^3 1 + 3(1)^2 = 2 ( ₀ M 4 r^3 ) B_ pole = 2 B_ eq B_ pole = 2 3.4 10⁻⁵ T = 6.8 10⁻⁵ T