Answer to Question #105178 in Electricity and Magnetism for Jeevan Jyoti behera

Question

Is the statement is true or false. Give reason. An electron moves in a magnetic field of 1T with velocity 5.0 x 10 raise power 5 m/s in the direction of the magnetic field. The magnitude of the force experienced by the electron is 9.5 x 10 raise power —14 N

Answer 1

Given:

$B=1\text{ T},\\ v=5\cdot10^5\text{ m/s},\\ F=9.5\cdot10^{-14}\text{ N}.$

Solution:

The words "in the direction of the magnetic field" are absolutely unclear. But seems like the electron moves along the field lines. What will be the force in that case?

$$F=evB\text{ sin}(v,B).$$

Since the angle between vectors v and B is 0 or 180, the sine is 0 and the force is 0. If the electron moves perpendicularly to the field lines, the force is

$$F=evB\text{ sin}(90^\circ)=8\cdot10^{-14}.$$

In these two cases the statement is wrong.