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Hi! I'm getting ready for an exam and want to make sure if I solved some problems correctly. I would be grateful for your feedback

After going through potential difference of 5000 V an electron falls in uniform magnetic field.

It’s induction is 0.1T and the electron’s speed is perpendicular to the lines of the magnetic field.

Find:

A. radius of the circle around which the electron will be moving

B. time it takes for the electron to travel one full circle.

K = eU = mv^2/2

F = mv^2/r = B*q*v

B = 0.1 T

U = 5000 V

Also if the electron is moving from left to right, and the magnetic field goes from top to bottom - Lorentz’s force would push it “into the screen”.

Since the kinetic energy of an electron K = eU = mv^2/2 we can find the speed.

e = 1.6*10^-19 J

m = 9.1*10^-31 kg

So v^2 = 2eU/m = (2*1.6*10^-19*5000)/(9.1*10^-31) = 1.75824176*10^15

v = sqrt(1.75824176*10^15) = 41931393.5 m/s

Because there’s centripetal magnetic force acting on the electron F = mv^2/r = B*q*v. Therefore r = mv/(B*q)

r = (9.1*10^-31*41931393.5)/(0.1*1.6*10^-19) = 2.38484801*10^-3 m

Or r = 2.38484801 mm.

To find the time we divide the length of the path by the speed, so

t = 2Pi*r/v = (2*3.14*2.38484801*10^-3)/41931393.5 = 3.57175001*10^-10 s

1. Homework Statement1. Homework Statement

After going through potential difference of 5000 V an electron falls in uniform magnetic field.

It’s induction is 0.1T and the electron’s speed is perpendicular to the lines of the magnetic field.

Find:

A. radius of the circle around which the electron will be moving

B. time it takes for the electron to travel one full circle.

## Homework Equations

K = eU = mv^2/2

F = mv^2/r = B*q*v

## The Attempt at a Solution

B = 0.1 T

U = 5000 V

Also if the electron is moving from left to right, and the magnetic field goes from top to bottom - Lorentz’s force would push it “into the screen”.

Since the kinetic energy of an electron K = eU = mv^2/2 we can find the speed.

e = 1.6*10^-19 J

m = 9.1*10^-31 kg

So v^2 = 2eU/m = (2*1.6*10^-19*5000)/(9.1*10^-31) = 1.75824176*10^15

v = sqrt(1.75824176*10^15) = 41931393.5 m/s

Because there’s centripetal magnetic force acting on the electron F = mv^2/r = B*q*v. Therefore r = mv/(B*q)

r = (9.1*10^-31*41931393.5)/(0.1*1.6*10^-19) = 2.38484801*10^-3 m

Or r = 2.38484801 mm.

To find the time we divide the length of the path by the speed, so

t = 2Pi*r/v = (2*3.14*2.38484801*10^-3)/41931393.5 = 3.57175001*10^-10 s

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