A 24 loop circular coil 22 cmcm in diameter lies in the xyxy...

A 24-loop circular coil 22 cmcm in diameter lies in the xyxy plane. The current in each loop of the coil is 7.6 AA clockwise, and an external magnetic field B⃗ =(0.55i^+0.60j^−0.65k^)TB→=(0.55i^+0.60j^−0.65k^)T passes through the coil. Determine the magnetic moment of the coil, μ⃗ μ→, in a component form. Determine the torque on the coil due to the external magnetic field in a component form. Determine the potential energy UU of the coil in the field (take UU = 0 at θθ = π/2π/2).

Transcript

00:01 Hi, here in this given problem first of all suppose this is the z axis in upward direction to the top of the page then perpendicular to the page this is x y plane x axis in the plane of paper y axis coming out of the plane of paper and the loop is lying in x y plane and it is carrying current in clockwise direction as seen from above.

00:30 Number of loops in this coil 15 its diameter that is 22 centimeters so its radius half of diameter means 11 centimeter or we can say 0 .11 meter.

00:55 Current passing through the coil 7 .6 ampere magnetic field in vector form 0 .55 i cap plus 0 .60 j cap minus 0 .65 k cap tesla.

01:16 In the first part of the problem we have to find magnetic moment of this coil mu will be given by in magnitude first of all magnetic moment mu will be given by n i a means n i into pi r square plugging in the known values for n this is 15 multiplied by the current 7 .6 pi 3 .14 r 0 .11 square.

01:49 So this magnitude of the magnetic moment comes out to be equal to 4 .33 ampere meter square and for its direction as this is clockwise so here it will behave like south pole and magnetic moment always goes from south to north in a direction opposite to the external magnetic field.

02:15 So as the magnetic moment is from south to north means it will be along negative z axis so we can say in vector form this is minus 4 .33 k cap ampere meter square which is the answer for the first part of this given problem here.

02:37 Then in the second part of the problem torque acting on this coil in vector form that is given by the cross product vector product of magnetic moment vector with the magnetic field vector...

Question

Please give Ace some feedback