A horizontal overhead powerline is at a height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is$(\mu _{0}=4\pi\times 10^{-7}\; T\: m\: A^{-1} )$ Option 1) $2.5\times 10^{-7}\; T\; northward$ Option 2) $2.5\times 10^{-7}\; T\; southward$ Option 3) $5\times 10^{-6}\; T\; northward$ Option 4) $5\times 10^{-6}\; T\; southward$

As we learnt in

Ampere's Law -

Total Current crossing the above area is $\left ( i_{1}+i_{2}-i_{3} \right )$

- wherein

Outward postive  $\bigodot$

Inward negative X

from Ampers's theorem

$\vec{B}(2\pi d) =\mu_0i\Rightarrow \vec{B}=\frac{\mu_0i}{2\pi d}$

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

$\vec{B}=50\times 10^{-7} T\:(south\:wards) =\:5\times 10^{-6}T$

Option 1)

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

Incorrect

Option 2)

$2.5\times 10^{-7}\; T\; southward$

Incorrect

Option 3)

$5\times 10^{-6}\; T\; northward$

Incorrect

Option 4)

$5\times 10^{-6}\; T\; southward$

Correct

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