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 $(a, 0)$.

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

Answer 1

Answer: (B)

$B=\frac{\mu_{0} I}{4 \pi} \frac{i}{a}\left[\sin 90^{\circ}+\sin (-\theta)\right]=\frac{\mu_{0}}{4 \pi} \frac{i}{a}(1-\sin \theta)$

$=\frac{\mu_{0} i}{4 \pi^{a}}\left(1-\frac{b}{\sqrt{a^{2}+b^{2}}}\right)$