Question

1. An electron (Q=16x10^-20 C, m=1x10^-30 kg) moving at half a megameter per second up the page enters a region with a uniform magnetic field of 1 T directed out of the page. Find the initial magnetic force magnitude and direction (in page coordinates) on the particle and find the radius of the curve it will follow.

Answer 1

Step-by-step explanation:

It is given that,

Charge on electron,
`q=16* 10^(-20)\ C`

Mass of the electron,
`m=9.1* 10^(-31)\ kg`

Speed of the electron,
`v=0.5\ Mm/s=0.5* 10^6\ m/s`

Magnetic field, B = 1 T (directed out of the page)

Let F is the magnetic force acting on the electron. It is given by :

`F=qvB\ sin\theta`

Here,
`\theta=90^(\circ)`

`F=qvB`

`F=16* 10^(-20)\ C* 0.5* 10^6\ m/s* 1\ T`

`F=8* 10^(-14)\ N`

Using the right hand rule, the direction of magnetic force is upward to the plane of the paper. Also, the electron will follow the circular path. It is given by :

`r=(mv)/(qB)`

`r=(9.1* 10^(-31)\ kg* 0.5* 10^6\ m/s)/(16* 10^(-20)\ C* 1\ T)`

`r=2.84* 10^(-6)\ m`

Hence, this is the required solution.