An infinitely long straight conductor carries a current of 150 A. At what distance from the conductor is the magnetic field caused by the current equal to \( 10^{-4} \) T?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.3 m
The magnetic field of an infinitely long straight current-carrying conductor at a perpendicular distance \( r \) follows from Ampere's circuital law (or the Biot-Savart law).
\( \displaystyle B = \frac{\mu_0 I}{2\pi r} \;\Rightarrow\; r = \frac{\mu_0 I}{2\pi B} \)
\( \mu_0 = 4\pi\times10^{-7}\,\mathrm{T\,m\,A^{-1}} \)
\( I = 150\,\mathrm{A} \)
\( B = 10^{-4}\,\mathrm{T} \)
\( \displaystyle r = \frac{4\pi\times10^{-7} \times 150}{2\pi \times 10^{-4}} = \frac{2\times10^{-7} \times 150}{10^{-4}} \)
\( \displaystyle r = \frac{3\times10^{-5}}{10^{-4}} = 0.3\,\mathrm{m} \)