Question

# Helmholtz coils are a method developed to provide a uniform magnetic field in a small region....

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?

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/2 R =348.84/2 x5x10-2

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