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Question: A horizontal overhead powerline is at height of \(4m\) from the ground and carries a current of \(10...

A horizontal overhead powerline is at height of 4m4m from the ground and carries a current of 100 A100\,A from east to west. The magnetic field is directly below it on the ground is (μ0=4π×10−7TmA−1)\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}Tm{A^{ - 1}}} \right)
A.2.5×10−7T2.5 \times {10^{ - 7}}T southward
B.5×10−6T5 \times {10^{ - 6}}T northward
C.5×10−6T5 \times {10^{ - 6}}T southward
D.2.5×10−7T2.5 \times {10^{ - 7}}T northward

Explanation

Solution

To solve this problem firstly we should learn about the Moving charges and Magnetism and the concepts behind these terms. We will also learn about the magnetic field by using these concepts and by using the formula behind, we can easily solve the problem and approach the answer.

Complete answer:
Magnetic Field: It is defined as the space around the magnet or current carrying conductor around which magnetic effects can be experienced. It is a vector quantity having both magnitude and direction also having S.I. unit Tesla (T)\left( T \right). Magnetic fields choose its application in electric motors and generators also in Transformer and generator.
Moving charges and Magnetic field: A charge produces a magnetic field if it is in motion. Magnetic fields can also interact with a moving charge. By Third law of motion, the moving charge must exert an equal and opposite force.
Amperes’ Law: The magnetic field created by an electric current ∝\propto to the size of that electric current with a constant of proportionality equal to the permeability of free space,

The magnetic field is
B=μ04π2IrB = \dfrac{{{\mu _0}}}{{4\pi }}\dfrac{{2I}}{r}
=10−7×2×1004=5×10−6T= {10^{ - 7}} \times \dfrac{{2 \times 100}}{4} = 5 \times {10^{ - 6}}T

Due to right hand palm rule, the magnetic field is directed towards the south.

So, the correct answer option C 5×10−6T5 \times {10^{ - 6}}T southward.

Note: The magnetic field has both a North pole and a south pole. Magnetic fields do not require medium to propagate, it can propagate even in vacuum, also the energy storing capacity of magnetic fields is greater than the electric field. Therefore, it is used in Transformers, motors and generators.