To understand why charged particles move in circles perpendicular to a magnetic

Question

To understand why charged particles move in circles perpendicular to a magnetic field and why the frequency is an invariant.

A particle of charge q and mass m moves in a region of space where there is a uniform magnetic field B =B0k^(i.e., a magnetic field of magnitude B0 in the +zdirection). (Figure 1) In this problem, neglect any forces on the particle other than the magnetic force.

If the resulting trajectory of the charged particle is a circle, what is , the angular frequency of the circular motion?

Express in terms of q, m, and B0.

Explanation / Answer

v = v i

B = B0 k

magnetic force is given as:

Fm = q ( v X B)        { Cross product }

Fm = q ( vi X B0 k) = - qvB0 j

force on this particle will always be perpendiculr to the velocity vector

(because of cross product)

hence particle will move into ciruclar motion.

Magnetic force = Centripetal force

qvB0 = m v^2 / r

r = m v / qB0

and w = v / r   = v / (m v / q B0 )

w = q B0 / m

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