Question

A beam of protons passes undeflected with a horizontal velocity v, through a region of electric and magnetic fields, mutually perpendicular to each other and normal to the direction of the beam. If the magnitudes of the electric and magnetic fields are 50 kV/m and 100 mT respectively; calculate the

(i) Velocity of the beam. 

(ii) Force with which it strikes a target on the screen, if the proton beam current is equal to 0.80 mA.

Answer 1

For a beam of charged particles to pass undeflected crossed electric and magnetic fields, the condition is that electric and magnetic forces on the beam must be equal and opposite i.e.,

\(eE=e\text{v}B\) \(\Rightarrow v=\frac{E}{B}\)

Given, E = 50k V/m = 50 x 10³ V/m

B = 100 mT = 100 x 10^-3 T