Question

What is the net force (magnitude and direction) on the electron moving in the magnetic field in figure below if B=2T; v= 4 x 10^4 m/s; `theta`=30°?

Answer 1

Force experienced by a charge `q` moving with velocity `vecv` in a magnetic field `vecB` is given by Lorentz Force equation

`vecF_M=q(vecvxxvecB)`

Inserting given values to find the magnitude of the force on an electron, ignoring the `-ve` sign of electronic charge as it is magnitude.

`|vecF_M|=q|vecv||vecB|sintheta`
`|vecF_M|= 1.6 xx 10^- 19 cdot 4 xx 10^4 cdot 2 cdot sin 30^@` `= 6.4 xx 10^-15 \N`

To find the direction of force, we observe that the vector `\vec{v}xx \vec{B}` is directed out of the page, using right hand rule. Therefore, for a negative charge of electron the cross product will be directed in the oppsite direction, opposite to this.

`=>vecF_M=6.4 xx 10^-15 \N`, directed into the page.