Question

An infinitely long wire carrying current $I$ is along Y-axis such that its one end is at point $A(0,b)$ while the wire extends upto $+\infty$. The magnitude of magnetic field strength at point $(a,0)$ is :

• A. $\frac{{\mu }_{0}I}{4\pi a}(1+\frac{b}{\sqrt{a^2+b^2}})$
• B. $\frac{{\mu }_{0}I}{4\pi a}(1-\frac{b}{\sqrt{a^2+b^2}})$
• C. $\frac{{\mu }_{0}I}{4\pi a}\left(\frac{b}{\sqrt{a^2+b^2}}\right)$
• D. none of these

Answer 1

The correct option is B $\frac{{\mu }_{0}I}{4\pi a}(1-\frac{b}{\sqrt{a^2+b^2}})$

$B=\frac{{\mu }_0}{4\pi }\frac{i}{a}[\sin 90+\sin (-\theta )]=\frac{{\mu }_0}{4\pi }\frac{i}{a}(1-\sin \theta )$
$=\frac{{\mu }_0}{4\pi }\frac{i}{a}(1-\frac{b}{\sqrt{a^2+b^2}})$ since $\sin \theta =\frac{b}{\sqrt{b^2+a^2}}$