Question

A long, straight wire 9.27 mm in diameter carries 147 A distributed uniformly over its cross section.Find the magnitude of the magnetic field (also called the magnetic field strength)

(a) 2.50 mm from the wire’s axis and

(b) 7.50 mm from the axis

Answer 1

a)

$$I=JA\\2\pi rB=\mu_0 J(\pi r^2)\\B=\mu_0 I\frac{r}{2R^2} \\B=4\pi\cdot10^{-7} (147)\frac{2.5\cdot10^{-3}}{8(9.27\cdot10^{-3})^2}=6.72\cdot10^{-4}\ T$$

b)

$$I=JA\\2\pi rB=\mu_0 J(\pi R^2)\\B=\mu_0 I\frac{1}{r} \\B=4\pi\cdot10^{-7} (147)\frac{1}{7.5\cdot10^{-3}}=2.46\cdot10^{-2}\ T$$