Question

Suppose I have a current source of 1.0 Amperes flowing through each of the following coils. What is the magnetic field in Tesla and in Gauss at the stipulated points? 1) At the center of a single 200-turn coil with a radius of 103 mm. 2) A the midpoint between two 200-turn coaxial coils of radii 103 mm and separated by a distance of 103 mm. (Assume the currents are arranged so that the fields add constructively). 3) At the center of a 565-turn, 146 mm-long solenoid of radius 34.1 mm.

Answer 1

1) at the centre of the coil B =(*n*i)/(2*R)

where is permeability of free space = 4**10-7 H/m

i current passing through the circular coil = 1.0A

R radius of the coil = 103mm = 0.103 m

n number of turns = 200

B = (4**10-7*200*1.0)/(2*0.103) = 400*3.14*10-7/0.103 = 1.22 * 10-3 T = 1.22mT

2) On the axis of a circular coil magnetic field

B = (*n*i*R2)/(2*(R2 +x2)3/2)

here given that mid way between two coil of seperation 0.103m i.e.,

x = 0.103/2 = 0.0515m

and field due to two coil.

hence B = 2* (*n*i*R2)/(2*(R2 +x2)3/2)

B = 2* (4**10-7*200*1.0*0.103*0.103)/(2*(0.103*0.103+0.0515*0.0515)3/2)

B= 2*0.003055 = 0.00611T = 6.11mT

3) length of solenoid = 146mm =0.146m

number of turns = 565

number of turns per unit length = 565/0.146 = 3869.86 = 3869 turn/m

magnetic field at the the centre of solenoid B = *n*i = 4**10-7*3869*1.0 =4.86mT