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,
[tex]F_c=\frac{mv^2}{r}[/tex]
Where,
m=mass
v=velocity
r=radius
In the other hand we have the magnetic force, defined by,
[tex]F_M=Bqv[/tex]
Where,
B=Magnetic Field
q= charge
v= Velocity.
In equilibrium we have that
[tex]F_c=F_M[/tex]
[tex]\frac{mv^2}{r} = Bvq[/tex]
Solving for have B,
[tex]B= \frac{mv}{qr}[/tex]
Our values are given by,
[tex]v=14200m/s\\r=0.0209m\\q=1.60218*10^{-19}c\\m=9.10939*10^{-31}Kg[/tex]
[tex]B=\frac{(9.10939*10^{-31})(14200)}{(1.60218*10^{-19})(0.0209m)}[/tex]
[tex]B= 3.8629*10^{-6}T}}[/tex]
Therefore the strength of the magnetic field inside the solenoid is [tex]3.8629*10^{-6}T}}[/tex]
