Question: Draw a picture of two horizontal parallel wires placed 1m apart and each carrying 1 ampere of current in the same direction.

a. At the upper wire what is the direction of the B field caused by the lower wire?

b. At the upper wire, what is the magnitude of the B field caused by the lower wire?

c. What is the direction of the force on the upper wire exerted by the B-field from the lower wire?

d. What is the average force on one electron in the wire? Assume the wires are 22-gauge copper (0.0644cm diameter); the density of electrons is 8.43 × 1022 cm^-3; and their average drift velocity is 2.27 × 10-4 m s^-1.

e. What is the force per meter on the wire?

f. Put your result for the force into algebraic form. Instead of numbers use n (the number density of free electrons), v (the drift velocity of the electrons), I (the electric current), A (the cross sectional area of the wire), and μ0 (the magnetic permeability of free space-the constant that appears in Eq. etc. Notice that your final result depends only on the current I and the distance between the wires, not on the electron density n or the area A of the wire. This fact allows the official definition of the ampere to be the amount of current that produces a force of 2 × 10-7 Nm^-1 between two long parallel wires 1 m apart and carrying the same current. (The coulomb is then officially defined to be the amount of charge carried past a point in 1 s by a current of 1 ampere.)

B(r) = μ₀I
         2πr'