Question

A segment of wire of total length 3.0 m carries a 15-A current and is formed into a semicircle. Determine the magnitude of the magnetic field at the center of the circle along which the wire is placed. a. 1.6 mu T b. 4.9 mu T c. 1.0 mu T d. 9.8 mu T e. 15 mu T

Answer 1

c. 1.0 mu T

Step-by-step explanation:

From, the ampere's circuit law:

∫B.dl = μ₀ I

B.(2πr) = μ₀ I

where,

B = Magnetic Field = ?

r = radius of the circle = length of wire = 3 m

μ₀ = Permeability of free space = 4π x 10⁻⁷ Tm/A

I = Current = 15 A

Therefore,

B(2π)(3 m) = (4π x 10⁻⁷ Tm/A)(15 A)

B = 10 x 10⁻⁷ T

B = 1 x 10⁻⁶ T = 1 μT

Hence, the correct option is:

c. 1.0 mu T