Question

Figure 32-38 shows a loop model (loop $\mathit{L}$) for a paramagnetic material. (a) Sketch the field lines through and about the material due to the magnet. What is the direction of (b) the loop’s net magnetic dipole moment $\overrightarrow{\mathbf{\mu }}$, (c) the conventional current $\mathit{i}$in the loop (clockwise or counterclockwise in the figure), and (d) the magnetic force acting on the loop?

Short answer

(a) The field lines through and about the material due to magnet are sketched.

(b) Direction of loop’s magnetic dipole moment $\overrightarrow{\mu }$is –x direction.

(c) Direction of conventional current $i$in the loop is counterclockwise.

(d) Magnetic force acting on loop is toward left.

Step-by-step solution

Understanding the concepts of magnetism:

By using the concept of para magnetism, energy stored in capacitor, energy stored in inductor as well as the rate of energy supply by the driving EMF, we can find the above quantities.

(a) Sketch the diagram:

Sketch the field lines through and about the material due to magnet.

(b) Explanation of direction of loop’s magnetic dipole moment:

For the paramagnetic material, the dipole moment $\overrightarrow{\mu }$ is in the same direction as of $\overrightarrow{B}$. From the above figure, it is clear that$\overrightarrow{\mu }$ points in the –x direction.

(c) Explanation of direction of conventional current:

From the right-hand rule, since $\overrightarrow{\mu }$points in the –x direction, the current flows counterclockwise from the perspective of the bar magnet.

(d) Explanation of magnetic force acting on loop:

The effect of $\overrightarrow{F}$ is to move the material toward regions of larger $\left|\overrightarrow{B}\right|$ values. Force is toward left directions.