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Force Magnetic

What is the relation between magnetic force on a ferromagnetic object and the magnetic field it is in?
Suppose there is a piece of metal close to a coil that generates a magnetic field with a strength equal to B(mag), the piece of metal experiences a magnetif force F(mag).
Were I to double the value of B(mag), will F(mag) increase by the same factor? By the square root of 2, the square of 2?
In other words: is the relation between B(mag) and F(mag) exponential, linear, logarithmic or something else?
Everything else equal; yes.
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Physical Science 6.8b - Magnetic Force on Moving Charge
What is the magnitude of the magnetic force?
A charge is moving perpendicular to a magnetic field and experiences a force whose magnitude is 2.08 x 10-3 N. If this same charge were to move at the same speed and the angle between its velocity and the same magnetic field were 40.1o, what would be the magnitude of the magnetic force that the charge would experience?
F = B x I Vector cross product
F= BqvSin(theta)
In the first case Theta is 90 degrees
in the second it is 40.1 degrees.
Use the equation twice, eliminate Bqv, to get the second force.
Don't just copy this - check it out in your book - to make sure you understand these peculiar forces which do no work!
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