Question

A charged particle is injected at 211 m/s into a 0.0633‑T uniform magnetic magnetic field perpendicularly to the field. The diameter of its orbit is measured and found to be 0.0389 m. What is the charge–to–mass ratio of this particle?

Answer 1

Answer:

$85.68*10^3C/kg$

Explanation:

For this problem we need the concept about Force in a Magnetic field,

For definition we know that

$F=m\frac{v^2}{r}$

Where v is the velocity, m the mass and r the radius or distance between the two points.

We know as well that

$F = qvB$

where q is the charge of a proton

v the velocity and B the magnetic field, then matching the two equation,

$qvB=m\frac{v^2}{r}$

Re-arrange for q/m (charge to mass ratio)

$\frac{q}{m} = \frac{v}{Br}$

Our values are,

$v=211m/s$

$B= 0.0633T$

$r=0.0389m$

Substituting,

$\frac{q}{m} = \frac{211}{0.0633*0.0389}$

$\frac{q}{m} = 85689.8 C/kg = 85.68*10^3C/kg$