Question

An electron and a second particle both move in circles perpendicular to a uniformmagnetic field. The mass of the second particle is the same as that of a proton but thecharge of this particle is different from that of a proton. If both particlestakethesameamount of time to go once around their respective circles, determine the charge of thissecond particle. You may use the values:melectron9.1110−31kg,qelectron1.6010−19C, andmproton1.6710−27kg.

Answer 1

Answer:

The change on the second particle is $2.93\times 10^{-16}\ C$.

Explanation:

The period of revolution of the particle in the magnetic field is given by the formula as follows :

$T=\dfrac{2\pi m}{Bq}$

It is given that the magnetic field is uniform. The mass of the second particle is the same as that of a proton but thecharge of this particle is different from that of a proton.

$m_s=m_p$

If both particles take the same amount of time to go once around their respective circles. So,

$T_e=T_s\\\\\dfrac{2\pi m_e}{Bq_e}=\dfrac{2\pi m_s}{Bq_s}\\\\\dfrac{m_e}{q_e}=\dfrac{m_p}{q_s}\\\\q_s=\dfrac{m_pq_e}{m_e}\\\\q_s=\dfrac{1.67\times 10^{-27}\times 1.6\times 10^{-19}}{9.11\times 10^{-31}}\\\\q_s=2.93\times 10^{-16}\ C$

So, the change on the second particle is $2.93\times 10^{-16}\ C$.