Question

A regular hexagon shaped wire loop with a side length of a = 41.0 cm carries an electric current of I = 12.0 A as shown in the figure.

Determine the size of the magnetic field at point Q, one of the vertices of the hexagon.

a P

Answer 1

given

a = 41.0 cm

= 0.41 m

I = 12.0 A

r = ( a/2 ) / tan30

r = ( 0.41/2 ) / tan30

r = 0.355 m

using equation magnetic field due to the rectangular of the hexagon is

B = n $\mu$ _o i sin ( $\pi$ /n ) / 2 $\pi$ r

B = 6 X 4 X 3.14 X 10^-7 X 12 X sin ( $\pi$ /6 ) / 2 X 3.14 X 0.355

B = 2.028 X 10^-5 T

the size of the magnetic field at point Q, one of the vertices of the hexagon is B = 2.028 X 10^-5 T