Question

A solenoid with 7 x 104 /m (turns per meter) runs through the x-y plane. Within the solenoid a charge of +3 coulombs with a mass of 4 grams is initially moving at 39 m/s in the +x direction. Due to the magnetic field created by the solenoid it orbits in a circle of radius 0.34 meters counter-clockwise. What's the amount, in amps, and direction of the current for the solenoid? If clockwise, input the current as negative.

Answer 1

magnetic field in solenoid=B=mu*n*I

where mu=magnetic permeability=4*pi*10^(-7)

n=number of turns per unit length=7*10^4

I=current

force on the moving charge=F=q*cross product of v and B

here v and B are perpendicular to each other

magnitude of force F=q*v*B

this force is balanced by cenitrpetal force=m*v^2/r

where r =radius of the circlular path

hence q*v*B=m*v^2/r

==>B=m*v/(q*r)

==>mu*n*I=m*v/(q*r)

==>I=m*v/(mu*n*q*r)

using the given values,

I=0.004*39/(4*pi*10^(-7)*7*10^4*3*0.34)=1.7387 A