Question

A particle with charge q and kinetic energy K travels in a uniform magnetic field of magnitude B. If the particle moves in a circular path of radius R, find expressions for each of the following. (Use any variable or symbol stated above as necessary.)

Answer 1

Answer:

Explanation:

In this question it is assumed that expressions for speed and mass are asked

Kinetic energy

$KE= 0.5mv^2$

since the charge moving in a circle

$qvB= mv^2/r$

So we can write

$v= \frac{2KE}{qBr}$

so, the expression for speed

$v= \frac{2KE}{qBr}$

now to obtain the expression for mass

Force F = m×a

and so solving for m we get:

plug expression for v back into KE equation

$KE= \frac{1}{2}m(\frac{2KE}{qBr})^2$

now rearranging the above equation we get

$m= \frac{(qBr)^2}{2KE}$