A conducting rod with a length ℓ = 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω as shown in the figure.The wire and the rod are in the plane of the page.A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and into the paper.An external applied force moves the rod to the right with a constant speed of 6.0 m/s.What are the magnitude and direction of the induced current in the circuit?
A)17 mA clockwise
B)17 mA counterclockwise
C)75 mA counterclockwise
D)75 mA clockwise
E)52 mA clockwise

Question

A conducting rod with a length ℓ = 25 cm is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of 8.0 Ω as shown in the figure.The wire and the rod are in the plane of the page.A constant uniform magnetic field of strength 0.40 T is applied perpendicular to and into the paper.An external applied force moves the rod to the right with a constant speed of 6.0 m/s.What are the magnitude and direction of the induced current in the circuit? 
A)17 mA clockwise 
B)17 mA counterclockwise 
C)75 mA counterclockwise 
D)75 mA clockwise 
E)52 mA clockwise

Quizplus · Accepted Answer

The magnetic force acting on the rod is given by F = BIL, where B is the magnetic field strength, I is the current induced in the circuit, and L is the length of the rod in the magnetic field. Since the rod is moving to the right, the induced current must be in the counterclockwise direction to produce a magnetic force to the left to balance the external force and maintain a constant speed. Therefore, we can use the equation for the induced EMF, ε = BLv, where v is the velocity of the rod, to find the induced current: I = ε/R = (BLv)/R. Substituting the given values, we get I = (0.40 T)(0.25 m)(6.0 m/s)/(8.0 Ω) = 75 mA, which is counterclockwise as discussed above. Therefore, the answer is (C) 75 mA counterclockwise.

A Conducting Rod with a Length ℓ = 25 Cm