A rectangular loop with a current is allowed to rotate about axis O (which is pe

Question

A rectangular loop with a current is allowed to rotate about axis O (which is perpendic­ular to the page). In the indicated orientation, the loop itself is perpendicular to the page and you are seeing only its top edge. It can be wired so that the current flows up on that top edge or down on that top edge (as indicated in the diagram). Additionally, the net torque on the loop is zero and the net force on the loop is zero in that orientation. Thus, the loop is in equilibrium! Before you continue with the question, you should make sure you understand why they are zero. If the current flows up across the top of the rectangular loop, is that equilibrium stable or unstable? Explain. If the current flows down across the top of the rectangular loop, is that equilibrium stable or unstable? Explain.

Explanation / Answer

In this case, the loop is perpendicular to the magnetic field. So, the vector A of loop is directly perpendicular to the vector B. Now By relation , we know

torque = B * I * A sin 0 = 0, As the angle between vector A and B is 0 degrees.

As torque is zero, it means no forces are acting on the loop , Hence forces are also zero.

a) If the current flows upward , that means using Fleming's left hand rule we find that direction of force is upward. Since the loop is rectangular it will develop same amount of force in the downward as on the other side of loop current is flowing opposite. And thus these will counter balance each other , and the system will remain be stable.

b) Here also the same effect will happen. Due to the shape of loop as , it is symmetric on each sides. So, there will always be counter balance of forces..And hence in this case also it will remain stable.

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