Two smooth, horizontal, parallel conducting rails are separated by . A light,…

PHYSICS · Multi-part · AP · Physics C: Electricity and Magnetism · Magnetic Fields and Electromagnetism · Magnetic Fields and Electromagnetism

Problem

Two smooth, horizontal, parallel conducting rails are separated by

0.50\,\text{m}

. A light, conducting rod of the same length rests on the rails and is free to slide without friction. The rails are connected to an external circuit that maintains a constant current of

5.0\,\text{A}

through the rod from one rail to the other. Beginning at point

A

, the rails pass through a uniform vertical magnetic field of magnitude

0.80\,\text{T}

that occupies a

0.30\,\text{m}

long stretch along the rails. At

t = 0

, the rod just touches point

A

and is pushed along the rails with a constant speed of

2.0\,\text{m\,s}^{-1}

in the direction toward the field region. (i) Obtain an expression for the length

\ell(t)

of the rod that lies inside the magnetic field for the time interval in which it is partially or fully immersed. (ii) Using your result from part (i), write an expression for the magnetic force

F(t)

acting on the rod during the same interval. (iii) Calculate the maximum value of the magnetic force experienced by the rod and state the instant at which this maximum occurs.

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