A compass needle oscillates 20 times per minute at a place where the dip is 45 ° and the magnetic field is B 1 . The same needle oscillates 30 times per minute at a place where the dip is 30 ° and magnetic field is B 2 . Then B 1 : B 2 is

Step-by-step solution

The frequency of oscillations of a magnetic needle in earth’s magnetic field is given as f = 1 2 π μ B H I , where, horizontal component of earth’s magnetic field B H = B cos θ , μ is the magnetic moment of the magnetic needle and I is moment of inertia of the magnetic needle about the axis about which it oscillates. Here, θ is angle of dip. As the same magnetic needle is used, so the value of magnetic moment and the moment of inertia will remain the same at the two places. Now,