Question

A compass originally points North; at this location the horizontal component of the Earth's magnetic field has a magnitude of 2e-5 T. A bar magnet is aligned East-West, pointing at the center of the compass. When the center of the magnet is 0.25 m from the center of the compass, the compass deflects 70 degrees. What is the magnetic dipole moment of the bar magnet?

Answer 1

Answer:

μ =5.40 A-m²

Explanation:

The components of the net magnetic field are the magnetic field of the dipole and the magnetic field of Earth, then from the right triangle, the deflection angle is computed by

tan θ = Bdipole / Bearth     ⇒   Bdipole = Bearth* tan θ  

Bdipole = 2e-5 T*tan 70° = 5.49e-5 T

The magnetic field at the location of the compass due to the dipole has a magnitude

Bdipole = (μ₀/4π)(2μ/r³)    ⇒    μ = Bdipole r³ / 2(μ₀/4π)

μ = (5.49e-5 T)(0.27m)³ / 2(1 × 10−7 T m² /(C m/s)) = 5.40 A-m²