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.
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 \( + z\).
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.
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.
When switch S in Fig. E25.29 is open, the voltmeter V reads 3.08 V. When the switch is closed, the voltmeter reading drops to 2.97 V, and the ammeter A reads 1.65 A. Find the emf, the internal resistance of the battery, and the circuit resistance R. Assume that the two meters are ideal, so they don’t affect the circuit.
Question: A positive point charge is placed near a very large conducting plane. A professor of physics asserted that the field caused by this configuration is the same as would be obtained by removing the plane and placing a negative point charge of equal magnitude in the mirror image position behind the initial position of the plane. Is this correct? Why or why not?
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