Question

To construct a solenoid, you wrap insulated wire uniformly around a plastic tube 10 cm in diameter and 60 cm in length. You would like a 2.2 −Acurrent to produce a 2.4 −kG magnetic field inside your solenoid.

What is the total length of wire you will need to meet these specifications?

Express your answer using two significant figures.

Answer 1

B = , ,where i is current and n = number of turns per meter

2.4 X10^3 X 10^(-4) T = 4 pi X 10^(-7) Weber/(Amp-mr) X 2.2 A X n

n = 2.4X10^(-1)T / (4 pi X 10^(-7) x 2.2) = 0.09 X 10^6 = 9.0X 10^4 turns per meter

For each turn you require length of wire = 2 pi r = 2 pi (0.05m) = 0.1 pi meters

Total number of turns = 9.0 X 10^4 turns/meter X 0.60 mrs =5.4 X 10^4 turns

Total length of wire = 5.4 X 10^4 turns X length of each turn = 5.4 X 10^4 X 0.1 X pi = 1.7 X 10^4 meters