Radius of curvature of 1 MeV electron in 1 Tesla B field

[tuathan]

i need to calculate radius of curvature of 1 MeV KE electron in 1 Tesla magnetic field.

r = mv / eB

what is the (relativistic) speed, v, of the electron? (ans: 0.941 c ??)

then i think you use p(rho) = mo. V / sqrt (1 - v^2 /c^2) = mv (ans: 7.59E-22 kg m/s)

e = 1.6E-19 C
B = 1

please show calculation of radius of curvature..

(expected value for r: 4.74E-03 m ??)

 

[hamster143]

Your answer seems to be correct.

http://en.wikipedia.org/wiki/Cyclotron#Mathematics_of_the_cyclotron

 

[thomate1]

To calculate the radius of curvature of a 1 MeV electron in a 1 Tesla magnetic field, we first need to determine the relativistic speed of the electron. Using the equation given, we can solve for v:

v = p / (m * sqrt(1 - (v^2 / c^2)))

Plugging in the given values, we get:

v = (7.59E-22 kg m/s) / (9.11E-31 kg * sqrt(1 - (0.941 c)^2))

Solving for v, we get:

v = 0.941 c

Now, we can use the equation r = mv / eB to calculate the radius of curvature. Plugging in the values for m, v, e, and B, we get:

r = (9.11E-31 kg * 0.941 c) / (1.6E-19 C * 1 T)

Solving for r, we get:

r = 4.74E-03 m

This is the expected value for the radius of curvature of a 1 MeV electron in a 1 Tesla magnetic field. This calculation also takes into account the relativistic effects on the speed of the electron.