Question

The magnetic field due to a current in a straight line wire segment of length $L$ at a point on its perpendicular bisector at a distance $r:(r>>L)$

• A. Decrease as $\frac{1}{r}$
• B. Decreases as $\frac{1}{r^2}$
• C. Decreases as $\frac{1}{r^3}$
• D. Approaches a finite limit as $r\to \infty$

Answer 1

The correct option is B Decreases as $\frac{1}{r^2}$

Magnetic field due to a finite current carrying wire is given by:

$B=\frac{{\mu }_{o}I}{4\pi r}(\sin {\theta }_1+\sin {\theta }_2)$

$=\frac{{\mu }_{o}I}{4\pi r}(2\times \frac{L/2}{\sqrt{(L/2{)}^2+r^2}})$

Using $r>>L$,

$B\approx \frac{{\mu }_{o}I}{4\pi r^2}$

Hence, option B is correct