A horizontal overhead powerline is at height of $4 \mathrm{~m}$ from the ground and carries a current of $100 \mathrm{~A}$ from east to west. The magnetic field directly below it on the ground is $\left(\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\right)$

• A

  $2.5 \times 10^{-7} \mathrm{~T}$ southward
• B

  $5 \times 10^{-6}$ T northward
• Correct answer
  C

  $5 \times 10^{-6} \mathrm{~T}$ southward
• D

  $2.5 \times 10^{-7}$ T northward

Solution

The magnetic field is $\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{2 \mathrm{I}}{\mathrm{r}}=10^{-7} \times \frac{2 \times 100}{4}=5 \times 10^{-6} \mathrm{~T}$
According to right hand palm rule, the magnetic field is directed towards south.

Hence, the correct answer is option: 'C'.