Question

A wooden ring whose mean diameter is 14.5 cm is wound with a closely spaced toroidal winding of 615 turns.

Compute the magnitude of the magnetic field at the center of the cross section of the windings when the current in the windings is 0.640 A .

Answer 1

given that :

mean diameter of wooden ring, d = 14.5 cm

radius of the wooden ring, r = 7.25 cm = 0.0725 m

number of turns, N = 615

current flowing in the winding, I = 0.64 A

the magnitude of the magnetic field at the center of the cross section of the windings which is given as :

B = ₀ n I                          { eq. 1 }

where, n = N / 2R

₀ = permittivity of free space = 4 x 10^-7 N/A²

so, B = ₀ N I / 2R                            { eq. 2 }

inserting the values in eq.2,

B = (4 x 10^-7 N/A²) (615) (0.64 A) / 2 (0.0725 m)

B = (2 x 10^-7 N/A²) (393.6 A) / (0.0725 m)

B = (787.2 x 10^-7 N/A) / (0.0725 m)

B = 10857.9 x 10^-7 Nm/A

B = 1.08 x 10^-3 T