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

 

Answers (1)

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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