Question

One hundred turns of a thin insulated wire are tightly wrapped around a cardboard ring-shaped core, thereby forming an essentially flat coil (with negligible length) with a diameter of 20.0 cm.

a) What current through the coil would produce a B-field at its center of 200 uT?           

b) That coil of wire is lying flat on this page that has a magnetic field, directed out of the page, increasing by 0.24 T every 12.0 s. Determine the magnitude of the emf in the coil.

Answer 1

Answer:

Given. diameter of the ring shaped coil d = 20.0 cm so radius is r = 10.0 cm = 0.1 m and N = 100.

(a) Mangnetic field is B = 200 x 10-6 T

Using Ampere's law, magnetic field at the center of the circular coil having N turnsis B = μ0NI/2r

Therefore, current I = 2r B/μ0 = 2(0.1 m) (200 x 10-6 T) / (4 x 10-7 T m/A) = 0.318 A.

(b) Emf generated in the coil is = , where is magnetic flux passing through the coil and which is NBA.

Area of the coil is A = r2 = (0.1)2 = 0.0314 m2

Therefore, emf = = N A = (100) (0.0314 m2) (0.24 T) / (12.0s) = 6.28 V.