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In the given figure, the cube is length l on each side. Four straight segments of wire ab, bc, cd and da form a closed loop that carries a current I = i_(0) in the direction shown. A uniform magnetic field of magnitude B = B_(0) is in the positive y direction. Determine the torque on the loop |
Answer» Solution :We will make closed loops in a PLANE by adding WIRES so that calculation is simple.  LOOP `ade`,`vec(M)_(1) = (1)/(2)l^(2)i_(0)(-hat(j))` Loop `cde`, `vec(M)_(2) = (1)/(2)l^(2)i_(0)(-hat(k))` Loop `ABCE`, `vec(M)_(3) = l^(2)hat(i)_(0)(-hat(i))` `vec(M) = vec(M)_(1) + vec(M)_(2) + vec(M)_(3) = - (l^(2)i_(0))/(2)(2 hat(i) + hat(j) + hat(k))` `vec(B) = B_(0) hat(j)` `vec(tau) = vec(M) xx vec(B) = - (l^(2)B_(0)i_(0))/(2)[2(hat(i) xx hat(j)) + (hat(j) xx hat(j)) + (hat(k) xx hat(j))]` `= -(l^(2) B_(0)i_(0))/(2) [2 hat(k) - hat(i)] = (l^(2)B_(0)i_(0))/(2)(hat(i) - 2 hat(k))` `|vec(tau)| = tau = (l^(2) B_(0)i_(0))/(2) sqrt(5)` |
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