Question

A long solenoid has a 60 cm length, with 3000 circular turns. The diameter of each circular turn is 2cm. When the current travels through the solenoid, a .35 Tesla field is created inside.

A. How much current is traveling through this solenoid?

B. The diameter of this solenoid is decreased to 1cm. Using the current in Part A, what is the magnetic field magnitude now?

C. If this solenoid is created by a fixed length of wire, so that decreasing the diameter of each loop increases the number of loops, would your answer in part B change? Why or why not?

2. A long solenoid has a 60 cm length, with 3000 circular turns. The diameter of each circular turn is 2 cm. When current travels through the solenoid, a 0.35 Tesla field is created inside A. How much current is traveling through this solenoid? (56 A) B. The diameter of this solenoid is decreased to 1 cm. Using the current in part (A), what is the magnetic field magnitude now? c. If this solenoid is created by a fixed length of wire, so that decreasing the diameter of each loop increases the number of loops (while keeping the turn density constant), would your answer in part (B) change? Why or why not?

Answer 1

given
L = 60 cm = 0.60 m
N = 3000 turns
B = 0.35 T

A) use, B = mue*N*I/L

==> I = B*L/(mue*N)

= 0.35*0.6/(4*pi*10^-7*3000)

= 55.7 A

= 56 A

B) magnetic field does not depend on diameter of the solenoid.

so, B remains same.

C) No. the answer would not change.

N1*pi*d1 = N2*pi*d2

N2 = N1*(d1/d2)

= 3000*2/1

= 6000 turns

when N/d is constant, length of the solenoid becomes double.

so, B = mue*N2*I/L2

= mue*2*N*I/(2*L)

= mue*N*I/L

= 0.35 T

so, the answer would not change.