Question

<module 4a
interaction of a current loop with a magnetic field
the effects due to the interaction of a current - carrying loop with a magnetic field have many applications, some as common as the electric motor. this problem illustrates the
figure
view from the side
part a
will the interaction of the current through the loop with the magnetic field cause the loop to rotate?
view available hint(s)
yes, the net torque acting on the loop is negative and tends to rotate the loop in the direction of decreasing angle θ (clockwise)
yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle θ (counterclockwise)
no, the net torque acting on the loop is zero and the loop is in equilibrium
no, the net force acting on the loop is zero and the loop is in equilibrium
submit
part b complete previous part(s)
part c complete previous part(s)

Explanation:

Step1: Recall torque on current - loop formula

The torque on a current - carrying loop in a magnetic field is given by $\vec{\tau}=\vec{\mu}\times\vec{B}$, where $\vec{\mu} = NIA\hat{n}$ (magnetic dipole moment, $N$ is the number of turns, $I$ is the current, $A$ is the area of the loop, and $\hat{n}$ is the unit normal vector to the loop). When the magnetic field $\vec{B}$ and the magnetic dipole moment $\vec{\mu}$ are not parallel or anti - parallel, there is a non - zero torque.

Step2: Analyze the given situation

In the case of a current - carrying loop in a magnetic field as shown, if the loop is oriented such that the magnetic field and the normal to the loop have an angle between them, there will be a torque. The torque will cause the loop to rotate. The direction of the torque is determined by the right - hand rule for the cross - product $\vec{\tau}=\vec{\mu}\times\vec{B}$. If the loop is in a position where the forces on the sides of the loop create a net torque, it will rotate. When the loop is not in a position of stable or unstable equilibrium (where the net torque is zero), it will rotate. Here, since the loop is not in a state where the net torque is zero, it will rotate. The direction of rotation depends on the orientation of the current, the magnetic field, and the loop. If we assume the standard orientation and use the right - hand rule, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle $\theta$ (counterclockwise).

Answer:

Yes, the net torque acting on the loop is positive and tends to rotate the loop in the direction of increasing angle $\theta$ (counterclockwise)