1.

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 ?

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.


Discussion

No Comment Found

Related InterviewSolutions