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44E.

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Found in: Page 950

### University Physics with Modern Physics

Book edition 14th edition
Author(s) Hugh D. Young, Roger A. Freedman
Pages 1596 pages
ISBN 9780321973610

# Both circular coils A and B (Fig. E27.44) have area $$A$$ and $$N$$ turns. They are free to rotate about a diameter that coincides with the $$x$$ axis. Current $$I$$ circulates in each coil in the direction shown. There is a uniform magnetic field $$\vec B$$ in the $$+ z$$ direction. (a) What is the direction of the magnetic moment $$\vec \mu$$ for each coil? (b) Explain why the torque on both coils due to the magnetic field is zero, so the coil is in rotational equilibrium.(c) Use Eq. (27.27) to calculate the potential energy for each coil.(d) For each coil, is the equilibrium stable or unstable? Explain.

(a) Magnetic moment in coil A is directed along $$- z$$ axis and the magnetic moment in B is directed along $$+ z$$ axis.

See the step by step solution

## Step 1: Given data

Area of each coil is $$A$$.

Number of turns of each coil is $$N$$.

Current in each coil is $$I$$.

Direction of magnetic field $$\vec B$$ is $$+ z$$.

## Step 2: Direction of magnetic moment

The direction of magnetic moment can be obtained from the right hand rule. If the four fingers are closed in the direction of the rotating current, the open thumb points in the direction of the magnetic moment.

## Step 3: (a) Determination of magnetic moment of the two coils

In coil A, the current rotates in a clockwise direction, the magnetic moment thus points in the $$- z$$ direction. In coil B, the current rotates in an anti-clockwise direction, the magnetic moment thus points in the $$+ z$$ direction.