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:
$F_c = \frac{mv^2}{r}$

m = mass (kg)

v = velocity (m/s)

r = radius (m)

Fc = Centripetal force (N)

Since we are given its period:
$T = \frac{2\pi r}{v}\\\\v = \frac{2\pi r}{T}$

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

$q\frac{2\pi r}{T} B = \frac{m}{r}(\frac{2\pi r}{T})^2$

Cancel out the expression.

$qB = \frac{m}{r} (\frac{2\pi r}{T})$

Cancel out 'r'.

$qB = \frac{2\pi m}{T}$

Now, we can simplify as necessary to find a value for 'q' over 'm':
$\frac{q}{m} = \frac{2\pi }{TB} = \frac{2\pi }{(4.79 \times 10^{-6})(0.775)} = \boxed{1692554.464}$

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