Ampere's Law (Calculus) Video Lessons

Concept

# Problem: An electric current is flowing through a long cylindrical conductor with radius a = 0.15 m. The current density J= 5.5 A/m2 is uniform in the cylinder. In this problem we consider an imaginary cylinder with radius r around the axis AB (a) Express B in terms of J, a, and r.(b) For r = 2a, calculate the numerical value of B in Tesla

###### FREE Expert Solution

The magnetic field at r > a:

$\overline{){\mathbf{B}}{\mathbf{=}}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{\pi }\mathbf{r}}}$

(a)

B = μ0(πa2J)/(2πr) = μ0a2J/2r

Th magnetic field is μ0a2J/2r

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###### Problem Details

An electric current is flowing through a long cylindrical conductor with radius a = 0.15 m. The current density J= 5.5 A/m2 is uniform in the cylinder. In this problem we consider an imaginary cylinder with radius r around the axis AB

(a) Express B in terms of J, a, and r.

(b) For r = 2a, calculate the numerical value of B in Tesla