When positioned 10 cm from the needle, a short magnet causes a 37^ deflection in a deflection magnetometer set in the Tan-A position. At what separation must the magnet be placed to produce a 37^ deflection of the needle if the magnetometer is instead used in the Tan-B position with the same magnet?

Step-by-step solution

In the Tan-A position, the magnetic field at the needle due to a short magnet at distance d₁ is given by: B_A = ₀ 4 2M d₁^3 The deflection is given by B_A = B_H . In the Tan-B position, the magnetic field at the needle due to the same short magnet at distance d₂ is given by: B_B = ₀ 4 M d₂^3 The deflection is given by B_B = B_H . Since the deflection is 37^ in both cases, the magnetic fields must be equal: B_A = B_B ₀ 4 2M d₁^3 = ₀ 4 M d₂^3 2 d₁^3 = 1 d₂^3 d₂^3 = d₁^3 2 d₂ = d₁ 2^ 1/3 Given d₁ = 10 cm and using 2^