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

Explanation:

It is given that,

Charge on electron, $q=16\times 10^{-20}\ C$

Mass of the electron, $m=9.1\times 10^{-31}\ kg$  

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

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, $\theta=90^{\circ}$

$F=qvB$    

$F=16\times 10^{-20}\ C\times 0.5\times 10^6\ m/s\times 1\ T$  

$F=8\times 10^{-14}\ N$

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 :

$r=\dfrac{mv}{qB}$

$r=\dfrac{9.1\times 10^{-31}\ kg\times 0.5\times 10^6\ m/s}{16\times 10^{-20}\ C\times 1\ T}$

$r=2.84\times 10^{-6}\ m$

Hence, this is the required solution.