What is the magnitude of the magnetic force on a charged particle?

Question

BlackTom AI · Accepted Answer

To determine the magnitude of the magnetic force on a moving charged particle, recall the Lorentz force for a particle with charge q moving with velocity v in a magnetic field B: F = q v × B, whose magnitude is F = |q| v B sin θ, where θ is the angle between v and B.
Option a states F = |q| v B cos θ, which is incorrect because the magnitude depends on sin θ, not cos θ, for the cross product between velocity and magnetic field.
Option b states F = |q| v B sin θ, which matches the correct magnitude expression derived from the cross product; this is the proper formula for the magnetic force magnitude on a moving charge.
Option c states F = I L B sin θ, which resembles the magnetic force on a current-carrying wire, not on a single moving charged particle; it uses current I and length L, making it inapplicable to a single particle scenario.
Option d states F = q v B sin θ. While it has the right sin θ factor, it omits the absolute value on q. Since force magnitude uses the absolute value of the charge to yield a nonnegative magnitude, this form can be ambiguous about sign and is not the standard magnitude expression.
Thus, the option that correctly represents the magnitude is the one with the absolute value of q: F = |q| v B sin θ.

UCIC 202503 PHYS101 Quiz 11

What is the magnitude of the magnetic force on a charged particle?

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