Question

A current ‘I’ is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing along a similar parallel wire 5m apart, in the negative Z-direction. A point P is at a perpendicular distance 3m from the first wire and 4 m from the second. What will be magnitude of the magnetic field $\vec{B}$ at P?

• A. $\frac{5}{12}\left({\mu }_{0^I}\right)$
• B. $\frac{7}{24}\left({\mu }_{0^I}\right)$
• C. $\frac{5}{24}\left({\mu }_{0^I}\right)$
• D. $\frac{25}{288}\left({\mu }_{0^I}\right)$

Answer 1

Answer: (C)

$B_1=magneticfieldduetofirstwire=\frac{{\mu }_0\times I}{2\pi \times 3}$
$B_2=magneticfieldduetosecondwire=\frac{{\mu }_0\times I}{2\pi \times 4}$
$B=netmagneticfield=\sqrt{B_1^2+B_1^2}=\frac{{\mu }_{0}I}{2\pi }\sqrt{\frac{1}{9}+\frac{1}{16}}=\frac{{\mu }_{0}I\times 5}{2\pi \times 3\times 4}=\frac{5}{24}\times \frac{{\mu }_{0}I}{\pi }$
$B=\frac{5}{24\pi }{\mu }_{0}I;buttheexactanswerisnotgiven,sobestpossibleanswerisC$