When placed at a separation of 10 cm from the needle, a short magnet causes a deflection of 37^ in a deflection magnetometer in the Tan-A position. Determine the ratio of the magnet's magnetic moment to the earth's horizontal magnetic field.

Step-by-step solution

In the Tan-A position, the magnetic field B due to a short magnet on its axial line is given by: B = ₀ 4 2M d^3 The deflection is given by the relation: B = B_H Equating the two expressions for B : ₀ 4 2M d^3 = B_H Rearranging to find the ratio M B_H : M B_H = d^3 2 ( ₀ 4 ) Substituting d = 10 cm = 0.1 m , = 37^ , and ₀ 4 = 10⁻⁷ T m/A : M B_H = (0.1)^3 37^ 2 10⁻⁷ Using 37^ = 3 4 = 0.75 : M B_H = 10⁻³ 0.75 2 10⁻⁷ M B_H = 0.75 2 10^4 M B_H = 0.375 10000 = 3750 A m ^2/ T