Question

Helmholtz coils are a method developed to provide a uniform magnetic field in a small region. They are constructed by placing two identical wire loops parallel to each other, separated by a distance equal to their radii, as shown in the Figure. Assume that the two loops are also connected in parallel to a power supply, so that they produce the same field.

(a) Find the length of a 28-gauge copper wire that will produce a 75 Ω coil.
m
[Use the American Wire Gauge information on Wikipedia to help solve this.]

If each coil has a 5 cm radius, then how many full turns of wire must you wind onto the spool to produce this resistance?


(c) If your power supply has a maximum output of 30 V, then what is the maximum current that will flow through the coils?
A

(d) What is the magnetic dipole moment of one of the coils?
A·m²

(e) What is the magnetic field at the midpoint of the line that connects the centers of the coils?

Answer 1

cross section 28AWG = 0.08mm²

resistance R = L/A

=resistivity of copprer =1.72x10^-8

L= length ?

A= area of cross section in m² =0.08x10^-6

R =75 Ω

L =RA/ =75x0.08x10^-6 /1.72x10^-8=348.84metre

b) number of turns = total lengthof wire / perimetre of single turn

T= L/2R =^348.84/2x5x10^-2

number of turns T= 1110.38 =1110 turns

c) maximum current I = V/R =30/75 =0.4 A

D)  magnetic dipole moment = area of turns x current = = R² xI =x(5x10^-2)² x0.4 =3.14x10^-3 Am²