Question

A beam of charged particles consisting of electron and protons are moving in +x direction and enter a region of uniform magnetic field in +y direction. If the protons are deflected in radius of 9.75ₓ10-2 m radius, calculate

a) The magnitude of the magnetic field

b) The radius that electron will be deflected and draw the schematic of the problem.

c) The electric field that should be applied so that the protons remain undeflected (both magnitude and direction)

Answer 1

a] The force on the protons due to the magnetic field will be:

F = qvBsin90

this force will be equal to the centripetal force

mv²/r = qvB

=> B = mv/qr

substitute the values of m, q and r to get:

B = [1.07 x 10^-7 v] T

where v is the velocity of the protons

b] r = mv/qB

since the charge on proton = charge on electron,

r = 5.313 x 10^-5 m

this is the radius of the path of electron.

c] The force on the proton will be directed along positive z direction and so the electric field must be directed downwards and must have the magnitude:

E = vB = [1.07 x 10^-7 v²] N/C

so that the proton goes undeflected.