Question

Electric rail cars often use magnetic braking. The brake consists of a set of electromagnets that are held just above the rails. To brake the train, the electromagnets are switched on, creating a magnetic field that induces eddy currents in the metal rails passing beneath them. In the figure, which of the choices correctly represents the eddy currents induced in the rails? The diagrams represent a view from above, looking down at the rail through the electromagnet. The electromagnet moves to the right, and the magnetic field points into the screen.

Choose the correct answer A,B,C, or D

Electric rail cars often use magnetic braking. The brake consists of a set of electromagnets that are held just above the rails. To brake the train, the electromagnets are switched on, creating a magnetic field that induces eddy currents in the metal rails passing beneath them. In the figure, which of the choices correctly represents the eddy currents induced in the rails? The diagrams represent a view from above, looking down at the rail through the electromagnet. The electromagnet moves to the right, and the magnetic field points into the screen.Choose the correct answer A,B,C, or D Details views of electromagnet and rail, seen from above Moving electromagnet (from above; transparent) Eddy currents in rail

Answer 1

Concepts and reason

The concept of magnetic flux, Lenz’s law, and eddy currents is required to solve the problem.

Initially, determine the change in magnetic flux at the leading and trailing edges of electromagnet. Later, determine the direction of induced magnetic field by using Lenz’s law. Finally, determine the direction of eddy currents by using right hand thumb rule.

Fundamentals

Eddy current is a swirling current induced within conductors by a changing magnetic field in the conductor.

Lenz’s law states that the current induced in a circuit due to a change in the magnetic field and the direction of induced current is such as to oppose the change in the magnetic field that produces it.

According to right hand thumb rule, curl the fingers of right hand into a half circle in such a way that the thumb points in the direction of the magnetic field, then the fingers will point in the direction of current.

(a)

As the electromagnet passes over the trails, the magnetic flux is changing under the leading and trailing edges of the electromagnet.

At the trailing edge magnetic flux is decreasing. Then by Lenz’s law a current is induced in such a way that it will increase the magnetic flux. Thus, at the leading edge the induced magnetic field must be into the screen. In figure (A), the induced current at the trailing edge is in a clockwise direction which implies that the induced magnetic field is into the screen.

At the leading edge magnetic flux is increasing. Then by Lenz’s law a current is induced in such a way that it will decrease the magnetic flux. Thus, at the leading edge the induced magnetic field must be out of the screen. In figure (A), the induced current at the leading edge is in a clockwise direction which implies that the induced magnetic field is into the screen and this violates the Lenz’s law.

(c)

At the trailing edge magnetic flux is decreasing. Then by Lenz’s law a current is induced in such a way that it will increase the magnetic flux. Thus, at the leading edge the induced magnetic field must point into the screen. In figure (C), the induced current at the trailing edge is in anticlockwise direction which implies that the induced magnetic field is out of the screen which violates the Lenz’s law.

(d)

At the trailing edge magnetic flux is decreasing. Then by Lenz’s law a current is induced in such a way that it will increase the magnetic flux. Thus, at the leading edge the induced magnetic field must be into the screen. In figure (D), the induced current at the trailing edge is in anticlockwise direction which implies that the induced magnetic field is out of the screen and this violates the Lenz’s law.

At the leading edge magnetic flux is increasing. Then by Lenz’s law a current is induced in such a way that it will decrease the magnetic flux. Thus, at the leading edge the induced magnetic field must be out of the screen. In figure (D), the induced current at the leading edge is in clockwise direction which implies that the induced magnetic field is into the screen and this violates the Lenz’s law.

(b)

At the trailing edge magnetic flux is decreasing. Then by Lenz’s law a current is induced in such a way that it will increase the magnetic flux. Thus, at the leading edge the induced magnetic field must be into the screen. In figure (B), the induced current at the trailing edge is in clockwise direction which implies that the induced magnetic field is into the screen. This agrees with the Lenz’s law.

At the leading edge magnetic flux is increasing. Then by Lenz’s law a current is induced in such a way that it will decrease the magnetic flux. Thus, at the leading edge the induced magnetic field must be out of the screen. In figure (B), the induced current at the leading edge is in anticlockwise direction which implies that the induced magnetic field is out of the screen. This also agrees with Lenz’s law.

Hence, the direction of current at the leading edge is clockwise and at trailing edge is anticlockwise.

Ans:

The following figure is incorrect.

The following figure is correct.