Physics Question about a wire and coil and the number of turns the coil makes.

Question

The radius of a coil wire with N turns is r=0.22m. A clockwise current of I coil= 2.0 A flows in the coil. A long straight wire carrying a current I wire= 31 A toward the left is located 0.05 m from the edge of the coil. The magnetic field at the center of the coil is zero tesla. Determine N, number of turns.

Answer 1

The magnetic fields from both sources located at the center of the coil would have be equal in magnitude, but opposite in direction.

The magnetic field at a distance r away from a long, current carrying wire is given by:

B = µ₀I / 2πr

At the center of the coil, the magnetic field from the long wire is:

B = ((4π x 10^-7 Tm/A) x 31 A) / (2π x (0.05 m + 0.22 m)) = 23 µT

Using the formula for the magnetic field of a coil of wire with N turns, solve for the number of turns:

N = 2πrB / µ₀I

= (2π x 0.22 m x (23 x 10^-6 T)) / ((4π x 10^-7 Tm/A) x 2.0 A)

= 13 turns