Need help solving the following problem, show all work needed please Proof Set 4

Question

Need help solving the following problem, show all work needed please

Proof Set 4 1.) The figure below shows a wood cylinder of mass 0.5kg and a length of 0.15 with N =10 turns of wire wrapped around it longitudinally, so that the plane of wire coil contains the axis of the cylinder. What is the least current I through the coil that will prevent the cylinder from rolling down the plan inclined at an angle e to the horizontal, in the presence of a vertical, uniform magnetic field of magnitude of O.ST, if the plane of the coil is parallel to the incline plane?

Explanation / Answer

torque due to gravity is balanced by the magnetic torque

magnetic torque T = mu B sin theta

T = N i d L B sin theta

torque due to gravity T = r Fsin theta

T = d m g sin theta / 2

N i d L B sin theta =d m g sin theta / 2

i = m g / 2 N L B

i = 0.5 * 9.8 / (2 * 10 * 0.15 * 0.5)

i = 3.27 Amp

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