A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.40A ,

Question

A rectangular coil of wire, 22.0 cm by 35.0 cm and carrying a current of 1.40A , is oriented with the plane of its loop perpendicular to a uniform 1.50T magnetic field, as shown in the figure I)Calculate the net force which the magnetic field exerts on the coil. II)Calculate the torque which the magnetic field exerts on the coil. iii)The coil is rotated through a 30.0 angle about the axis shown, the left side coming out of the plane of the figure and the right side going into the plane. Calculate the net force which the magnetic field now exerts on the coil. (Hint: In order to help visualize this 3-dimensional problem, make a careful drawing of the coil when viewed along the rotation axis.)

Explanation / Answer

F = i(L) x B = 1.4(2*0.22)(1.5)(sin 90) = 0.92 Newtons, I assumed the short side of the loop was perpendicular to the magnetic field. Half the force is on each 22 cm wire. If the long side is perpendicular the answer is 1.4(2*0.35)(1.5)(sin 90) = 1.47 Newtons. The torque in the first case is (1/2)(F)(D) = (0.5)(0.92)(0.35)(sin 90) = 0.161 newton meters. And if the long side is perpendicular to the magnetic field, T = (0.5)(1.47)(0.22)(sin 90) = 0.161 newton meters. They are equal as they should be. Torque = I(A) x B where I is the current in the loop, A the area of the loop, and B the magnetic field density. x is the cross product, sine of the angle between the loop perpendicular and the magnetic field. if you rotate the loop 30 degrees, sine 30 is 1/2 so the torque drops by 50%. Torque = (1/2)F x D (1/2) (0.92)(0.35) (sin 30)= 0.08 mewton meters

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