Question

A horizontal overhead powerline is at a height of $4m$ from the ground and carries a current of $100A$ from east to west. The magnetic field directly below it on the ground is : $({\mu }_0=4\pi \times {10}^{-7}Tm{A}^{-1})$

• A. $5\times {10}^{-6}T$ southward
• B. $2.5\times {10}^{-7}T$ northward
• C. $2.5\times {10}^{-7}T$ southward
• D. $5\times {10}^{-6}T$ northward

Answer 1

The correct option is A $5\times {10}^{-6}T$ southward

Magnetic field around a current carrying wire at a distance $r$ is given by ,

$B=\frac{{\mu }_{0}i}{2\pi r}$

$=\frac{4\pi \times {10}^{-7}\times 100}{2\pi \times 4}T$

$=5\times {10}^{-6}T$

The direction of magnetic field is found out by curling the fingers of the right hand around the wire when the thumb points towards the current carrying direction.

When fingers are wrapped with thumb pointing towards west, the fingers curl around the wire to point south at the lowest point touching ground.