Question

A long wire carrying current \( / \) is placed along perpendicular to plane shown in figure. The line integral \( \int \bar{B} \cdot \overline{d l} \) from point \( A \) to \( C \) is \( \frac{\mu_{0} l}{n} \). Find the value of \( n .(\bar{B} \) is magnetic field)

Answer 1

B = B₁ + B₂

B = \(\frac{HoI}{2\pi d}+\frac{HoI}{2\pi\,d/\sqrt3}\)

B = \(\frac{HoI}{2\pi}(\frac1d+\frac{\sqrt3}d)\)

Applying ampere's law:

\(\frac{HoI}{2\pi}(\frac{\sqrt3+1}d)\times\frac{2\pi d}{\sqrt3}=\frac{HoI}n\)

\(\frac{\sqrt3+1}{\sqrt3}=\frac1n\)

n = \(\frac{\sqrt3}{\sqrt3+1}\)