A solenoid in your car is 35 cm long and has a diameter of 8.0 cm. It is made of

Question

A solenoid in your car is 35 cm long and has a diameter of 8.0 cm. It is made of copper wire with a radius of 0.46 mm. The turns are closely packed and form a single layer. Assume the resistivity of copper is 1.68 times 10^-8 Ohm.m. When the solenoid is connected to your battery with sigma = 11.6 V, what is the magnetic field inside the solenoid? (Enter the magnitude.) If, instead, the turns form two layers, how does your answer change? (The solenoid is still 35 cm long to fit the car.) It would quadruple. It would not change. It would be a quarter of its original value. It would be a half of its original value. It would double.

Explanation / Answer

a)
R = 4 cm = 0.04 m
r = 0.46 mm = 4.6*10^-4 m
L = 35 cm = 0.35 m
Number of turns,N = L / (2*r)
length of wire L' = N*2*pi*R
A= pi*r^2
resistance,
R' = rho* L/A
= rho*N*2*pi*R/(pi*r^2)
= rho*N*2*R/(r^2)
= rho*L*2*R / (r^2*2*r)
= rho*L*R / (r^3)

cirrent, i = E/R'
  
B = N*miuo*i/L
=(L/2r)*miuo*(E*r^3/(rho*L*R)) *(1/L)
= E*miuo*r^2 / (2*rho*L*R)
=11.6*(1.2566*10^-6)*(4.6*10^-4)^2 / (2*1.68*10^-8*0.35*0.04)
=6.6*10^-3 T

b)
B = E*miuo*r^2 / (2*rho*L*R)
It world not change

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