A non-relativistic proton beam passes without deviation through a region of space where there are uniform transverse mutually perpendicular electric and magnetic fields with `E= 120 kVm^-1 and B=50 mT.` Then the beam strikes a grounded target. Find the force which the beam acts on the target if the beam current is equal to `i=0.8 mA`.
Mass of protons `= 1.67xx10^(-27) kg`.

Options

A. `80muN`
B. `25 muN`
C. `20 muN`
D. `35 muN`

Answer

c

Explanation

Since, proton moves with constant velocity . So, magnetic force on the proton is balanced by electric force.
`:. qE=qvB` or E=vB
The force on the target is `F=(Deltap)/(Deltat)=(mnv)/(Deltat)`
Where, n=number of protons before striking the target
`l=(n e)/(Deltat) implies n/(Deltat) =l/e`
`:. F=(mvl)/e =(ml)/e [E/B]`
`F=(1.6xx10^(-27)xx120xx1000xx0.8xx10^(-3))/(50xx10^(-3)xx1.6xx10^(-19))`
`=20xx10^(-6) N=20 mu N`