Torque on magnetic dipole in uniform field
- In a uniform magnetic field of 0.049 T, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is 9.8×10^-6 kg m^2. If the magnitude of magnetic moment of the needle is x×10^-5 Am^2; then the va… Answer: 1. 1280 π² Key idea: A magnetic needle in a field oscillates like a torsional pendulum: T=2π√(I/MB) . Period T=5/20=0.25 s. Squaring... 1
- If θ_1 and θ_2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given by : Answer: 4. cot²θ=cot²θ₁+cot²θ₂ Key idea: in a vertical plane at angle α to the magnetic meridian, tanθ'=tanθ/cosα , i.e. cotθ'=cotθcosα . Fo... 1
- A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is Answer: 1. sqrt3W Work to rotate a magnet from equilibrium ( θ=0 ) is W=MB(1-cosθ) ; torque at angle θ is τ=MBsinθ . W=MB(1-cos60^°)=MB/2 ,... 1