Question

A magnitic field is used to bend a beat of electrons. What uniform magnetic field is required to bend a beam of electrons moving at 1,2x10^6 m/s in a circular are of 0,25 m

Answer 1

The strength of the magnetic field is $2.73\cdot 10^{-5} T$

Explanation:

When a charged particle is moving in a uniform magnetic field, the particle experiences a force perpendicular to the direction of motion. This force is given by

$F=qvB$

where

q is the charge of the particle

v is the velocity of the particle

B is the strength of the magnetic field

Since this force acts perpendicular to the direction of motion, the particle moves in a circular motion and the force acts as a centripetal force, so we can write:

$F=qvB = m \frac{v^2}{r}$

where

m is the mass of the particle

r is the radius of the circular orbit

We can re-arrange the equation in order to isolate B:

$B=\frac{mv}{qr}$

In this problem, we have electrons, with

$m=9.11\cdot 10^{-31} kg$

$v=1.2\cdot 10^6 m/s$

$q=1.6\cdot 10^{-19} C$

r = 0.25 m

Substituting these numbers, we find the strength of the magnetic field:

$B=\frac{(9.11\cdot 10^{-31})(1.2\cdot 10^6)}{(1.6\cdot 10^{-19})(0.25)}=2.73\cdot 10^{-5} T$

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