Physics - Magnetism Question with Solution | TestHub

To find the magnetic field, consider the strip as an infinite number of thin wires. For a differential strip of width $dx$ at distance $x$ from the point, the current is $dI=I\frac{dx}{b}$. The magnetic field due to this strip is $dB=\frac{{\mu }_0}{2\pi }\frac{dI}{x}$. Integrating $dB$ from $a$ to $a+b$ gives $B=\frac{{\mu }_{0}I}{2\pi b}{\int }_a^{a+b}\frac{dx}{x}=\frac{{\mu }_{0}I}{2\pi b}[{\log }_{e}x{]}_a^{a+b}=\frac{{\mu }_{0}I}{2\pi b}{\log }_e\left(\frac{a+b}{a}\right)=\frac{{\mu }_{0}I}{2\pi b}{\log }_e\left(1+\frac{b}{a}\right)$.