Question

Figure shows a cross-section of a long ribbon of width $\omega$ that is carrying a uniformly distributed total current $i$ into the page. Calculate the magnitude and direction of the magnetic field $\overrightarrow{B}$ at a point P in the plane of the ribbon at a distance d from its edge.

Answer 1

$dB=\frac{{\mu }_o}{2\pi }\frac{\left(\frac{i}{\omega }\right)\cdot dx}{x}$

$B=\frac{{\mu }_{o}i}{2\pi \omega }{\int }_d^{d+w}\frac{dx}{x}$

$B=\frac{{\mu }_{o}i}{2\pi \omega }\ln \left(\frac{d+w}{d}\right)$ (upwards)