Question

A charged particle is injected at 109 m/s into a 0.0691‑T uniform magnetic field perpendicularly to the field. The diameter of its orbit is measured and found to be 0.0427 m. What is the charge–to–mass ratio of this particle?

Answer 1

We know, radius of the orbit is given by :

$r=\dfrac{mv}{qB}$

So, ratio is given by :

$\dfrac{q}{m}=\dfrac{v}{Br}\\\\\dfrac{q}{m}=\dfrac{109\ m/s}{0.0691 \ T \times 0.0427\ m}\\\\\dfrac{q}{m}=36942.01 \ C/kg\\\\\dfrac{q}{m}=3.69\times 10^{4}\ C/kg$

Therefore, the charge–to–mass ratio of this particle is $3.69\times 10^{4}\ C/kg$ .

Hence, this is the required solution.