The strength of the magnetic field is [tex]2.73\cdot 10^{-5} T[/tex]
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
[tex]F=qvB[/tex]
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:
[tex]F=qvB = m \frac{v^2}{r}[/tex]
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:
[tex]B=\frac{mv}{qr}[/tex]
In this problem, we have electrons, with
[tex]m=9.11\cdot 10^{-31} kg[/tex]
[tex]v=1.2\cdot 10^6 m/s[/tex]
[tex]q=1.6\cdot 10^{-19} C[/tex]
r = 0.25 m
Substituting these numbers, we find the strength of the magnetic field:
[tex]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[/tex]
Learn more about magnetic fields:
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