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

Answer:

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

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

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

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.