Question

A long vertical wire in which a current is flowing produces a neutral point with the Earth's magnetic field at a distance of $5cm$ from the wire. If the horizontal component of the Earth's magnetic induction is $0.18$ gauss, then the current in the wire is

• A. $0.45A$
• B. $4.5A$
• C. $0.9A$
• D. $0.036A$

Answer 1

Answer: (B)

$4.5A$

Magnetic field due to the wire is $0.18$ gauss
$1T={10}^4$ gauss
$\therefore B=\frac{{\mu }_{0}i}{2Ar}=0.18\times {10}^{-4}T$
$\frac{2\times {10}^{-7}\times i}{5\times {10}^{-2}}=0.18\times {10}^{-4}T$
$\frac{2}{5}i=1.8$
$i=4.5A$