Answer:
(a) B = 2.85 × [tex]10^{-6}[/tex] Tesla
(b) I = I = 0.285 A
Explanation:
a. The strength of magnetic field, B, in a solenoid is determined by;
r = [tex]\frac{mv}{qB}[/tex]
⇒ B = [tex]\frac{mv}{qr}[/tex]
Where: r is the radius, m is the mass of the electron, v is its velocity, q is the charge on the electron and B is the magnetic field
B = [tex]\frac{9.11*10^{-31*1.0*10^{4} } }{1.6*10^{-19}*0.02 }[/tex]
= [tex]\frac{9.11*10^{-27} }{3.2*10^{-21} }[/tex]
B = 2.85 × [tex]10^{-6}[/tex] Tesla
b. Given that; N/L = 25 turns per centimetre, then the current, I, can be determined by;
B = μ I N/L
⇒ I = B ÷ μN/L
where B is the magnetic field, μ is the permeability of free space = 4.0 ×[tex]10^{-7}[/tex]Tm/A, N/L is the number of turns per length.
I = B ÷ μN/L
= [tex]\frac{2.85*10^{-6} }{4*10^{-7} *25}[/tex]
I = 0.285 A
