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A rectangular loop consists of N closed wrapped turns and has dimensions a xx b. The loop is hinged along the y-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field B = B_(0) directed along the x-axis when current i = i_(0) in the direction shown. What is the expected direction of rotation of the loop ? |
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Answer» Solution :Area vector `vec(A) = vec(CO) xx vec(OA)` `= (-B cos 37^(@) hat(i) - b SIN 37^(@) hat(K)) xx (a hat(j))` `= -(ab)/(5)[4(hat(i) xx hat(j)) + 3(hat(k) xx hat(j))]` `= -(ab)/(5)[4hat(k) - 3hat(i)]` `= (ab)/(5) [3hat(i) - 4hat(k)]` MAGNETIC moment `vec(M) = N i_(0) vec(A)` `= (N i_(0) ab)/(5)(3hat(i) - 4hat(k))` `vec(B) = B_(0) hat(i)` `vec(tau) = vec(M) xx vec(B) = (N i_(0) ab B_(0))/(5)[3 (hat(i) xx hat(i)) - 4(hat(k) xx hat(i))]` `= -(4 N i_(0) ab B_(0))/(5) hat(j)` The loop will rotate in clockwise direction as seen from above. |
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