Question

An electron moving at right angles to a 0.14 T magnetic field experiences an acceleration of 6.5×1015 m/ s 2 . What is the electron's speed? Express your answer using two significant figures. By how much does its speed change in 1 ns( 10 −9 s) ?

Answer 1

`2.64\cdot 10^5 m/s`, the speed does not change

Step-by-step explanation:

The magnetic force on the electron is equal to the product between its mass and its acceleration:

`qvB = ma`

where

q is the electron charge

v is the electron speed

B = 0.14 T is the magnetic field

m is the electron's mass

`a=6.5\cdot 10^(15)m/s^2` is the acceleration (centripetal acceleration)

Solving for v, we find

`v=(ma)/(qB)=((9.11\cdot 10^(-31) kg)(6.5\cdot 10^(15) m/s^2))/((1.6\cdot 10^(-19) C)(0.14 T))=2.64\cdot 10^5 m/s`

The speed of the electron does not change, because the acceleration is a centripetal acceleration, so it acts perpendicular to the direction of motion of the electron; therefore, no work is done on the electron by the magnetic force, and therefore the electron does not gain kinetic energy, which means that its speed does not change.