Question

A charged particle moves in a uniform magnetic field of 0.775 T

with a period of 4.79×10−6 s.
Find its charge-to-mass ratio ||/.

Answer 1

Hi there!

Recall that a charge that enters a magnetic field while moving experiences a magnetic force that causes it to enter a state of uniform circular motion.

We know the following (For a point charge):

`F_B = qv B`

q = Charge (C)
v = velocity (m/s)
B = Magnetic field (T)

Fb= Magnetic force (N)

The equation for centripetal force:

`F_c = (mv^2)/(r)`

m = mass (kg)

v = velocity (m/s)

r = radius (m)

Fc = Centripetal force (N)

Since we are given its period:

`T = (2\pi r)/(v)\\\\v = (2\pi r)/(T)`

Plug this expression into the above equations. Since the magnetic force equals the centripetal force, set them equal to each other and simplify.

`q(2\pi r)/(T) B = (m)/(r)((2\pi r)/(T))^2`

Cancel out the expression.

`qB = (m)/(r) ((2\pi r)/(T))`

Cancel out 'r'.

`qB = (2\pi m)/(T)`

Now, we can simplify as necessary to find a value for 'q' over 'm':

`(q)/(m) = (2\pi )/(TB) = (2\pi )/((4.79 * 10^(-6))(0.775)) = \boxed{1692554.464}`

Thus, the charge is 1.693 ×10⁶ times larger than its mass.