   Chapter 19, Problem 68AP

Chapter
Section
Textbook Problem

A 0.200-kg metal rod carrying a current of 10.0 A glides on two horizontal rails 0.500 m apart. What vertical magnetic field is required to keep the rod moving at a constant speed if the coefficient of kinetic friction between the rod and rails is 0.100?

To determine
The vertical magnetic field required to keep the rod moving at a constant speed.

Explanation

Given info: The mass of the metal rod is 0.200kg . The current on the rod is 10.0A . The tow horizontal rails are separated by a distance 0.500m . The coefficient of kinetic friction between the rod and the rails is 0.100 .

Explanation:

For moving at constant speed, the rail should be at equilibrium. Hence the magnitude of the magnetic force must be equal to the friction force. Hence,

BILsinθ=μkmg

• B is the magnetic field
• I is the current in the top wire
• L is the length of the conductor
• θ is the angle between the magnetic field and the current element
• μk is the coefficient of kinetic friction
• m is the mass of the rod
• g is the free fall acceleration

On re-arrangement,

B=μkmgILsinθ

Substitute 0.100 for μk , 0.200kg for m , 9

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