Question

An electron circles at a speed of 14200 m/s in a radius of 2.09 cm in a solenoid. The magnetic field of the solenoid is perpendicular to the plane of the electron’s path. The charge on an electron is 1.60218 × 10−19 C and its mass is 9.10939 × 10−31 kg. Find the strength of the magnetic field inside the solenoid. Answer in units of T

Answer 1

To develop this problem we need to keep in mind the concept of centripetal energy and magnetic force.

The centripetal energy of a body by definition is given as,

`F_c=(mv^2)/(r)`

Where,

m=mass

v=velocity

r=radius

In the other hand we have the magnetic force, defined by,

`F_M=Bqv`

Where,

B=Magnetic Field

q= charge

v= Velocity.

In equilibrium we have that

`F_c=F_M`

`(mv^2)/(r) = Bvq`

Solving for have B,

`B= (mv)/(qr)`

Our values are given by,

`v=14200m/s\\r=0.0209m\\q=1.60218*10^(-19)c\\m=9.10939*10^(-31)Kg`

`B=((9.10939*10^(-31))(14200))/((1.60218*10^(-19))(0.0209m))`

`B= 3.8629*10^(-6)T}}`

Therefore the strength of the magnetic field inside the solenoid is
`3.8629*10^(-6)T}}`