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Question
What is the maximum magnitude of the force on an aluminum rod with a $0.100 \mu\textrm{C}$ charge that you pass between the poles of a 1.50 T permanent magnet at a speed of 5.00 m/s? In what direction is the force?

The magnitude of the force is $7.50 \times 10^{-7} \textrm{ N}$. It is in the direction perpendicular to both the magnetic field and the velocity.

Solution Video

# OpenStax College Physics Solution, Chapter 22, Problem 7 (Problems & Exercises) (1:32)

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This is College Physics Answers with Shaun Dychko. This charged Aluminum rod will experience a maximum force when it moves perpendicular to the magnetic field lines. And so, it could move downwards for example, like this. And if it does that, you would point your thumb in the downward direction. Your fingers to the right. And in the force would be in the direction of your palm which is out of the page. And the reason this works is because the charge is positive, 0.1 micro Coulombs and so this velocity is the direction of the motion of the positive charges. And so the Right Hand Rule gives the answer. If it was a negatively charged then it have to take the opposite answer to the Right Hand Rule. Okay, so the force is coming out of the page in the way I've drawn it here. And usually dots represent that force. These are arrow tips coming towards you out of the page. And the magnitude of force is the charge times the velocity times the magnetic field. This is for the maximum. You'd have a sine theta between them otherwise. But since theta is 90 degrees, sine of 90 is one. And so that factor doesn't affect anything. So we have 0.1 times ten to the minus six Coulombs charge times five meters per second times one and a half Tesla which gives 7.50 times ten to the minus seven Newtons will be the force.