As shown in the figure, an electron is fired with a speed of 3.33 106 m/s throug

Question

As shown in the figure, an electron is fired with a speed of 3.33 106 m/s through a hole in one of the two parallel plates and into the region between the plates separated by a distance of 0.18 m. There is a magnetic field in the region between the plates and, as shown, it is directed into the plane of the page (perpendicular to the velocity of the electron). Determine the magnitude of the magnetic field so that the electron just misses colliding with the opposite plate in units T.

As shown in the figure, an electron is fired with a speed of 3.33 106 m/s through a hole in one of the two parallel plates and into the region between the plates separated by a distance of 0.18 m. There is a magnetic field in the region between the plates and, as shown, it is directed into the plane of the page (perpendicular to the velocity of the electron). Determine the magnitude of the magnetic field so that the electron just misses colliding with the opposite plate in units T.

Explanation / Answer

KE = PE

0.5 mv^2 = eV

or v = sqrt(2eV/m)

apply centripetal force = magnetic force

i.e mv^2/r = qvB,

where m = mass o the charged particle

v = velocity,   r = radius ,

q = charge = 1.6*10^-19 C

B = magnetic field

so now as r = mv/qB

B = mv/qr

B = 9.11e-31* 3.33e6/(1.6e-19* 0.18)

B = 1.05*10^-4 T

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