Question

A 16.0 mm -long copper wire, 2.90 mmmm in diameter including insulation, is tightly wrapped in a single layer with adjacent coils touching, to form a solenoid of diameter 2.10 cmcm (outer edge).

A)What is the length of the solenoid?

B)What is the field at the center when the current in the wire is 19.0 AA ?

Answer 1

given

length of copper wire, L = 16.0 m
d = 2.90 mm = 0.29 cm
D = 2.1 cm (outer edge)

A)
mean radius of the solenoid, R_mean = (D/2) - (d/2)

= 2.1/2 - 0.29/2

= 0.905 cm

= 0.00905 m

number of turns, N = L/(2*pi*R_mean)

= 16/(2*pi*0.00905)

= 281

length of the solenoid, l = N*d

= 281*2.9 mm

= 815 mm (or) 81.5 cm (or) 0.815 m <<<<<<<<<<-------------Answer

B) magnetic field inside the solenoid,

B = mue*N*I/l

= 4*pi*10^-7*281*19/0.815

= 8.23*10^-3 T <<<<<<<<<<-------------Answer