A circular current carrying coil has a radius . The distance from the centre of the coil on the axis where the magnetic induction will be of its value at the centre of the coil is:

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answer is B.

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Detailed Solution

Concept- The formula for the magnitude of magnetic induction for a current carrying circular coil at a distance from its axis can be used to answer this question. We will next feed in the required value from the question and solve the equation to get the distance value. A current-carrying circular coil behaves like a two-poled magnet. The magnetic field value at x distance from the centre on its axis is given by,
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Where is the coil's current, is its radius, is the distance on the axis from its centre, and is the magnetic permeability of free space (vacuum) equal to

Let us now examine the question. The value of magnetic induction at a distance is given as

for the same coil's value at the centre, we must determine the distance.
Allow the distance to be

Now, using (1)
For magnetic induction at the centre,

. Putting this in (1) , we get,
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where

(centre) is the value of the magnetic induction at the centre.
Using (1) , magnetic induction at the distance

on the axis is given by,
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Now, by the problem

Therefore, putting

and (3) in (4) , we get,
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Putting cube root on both sides
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Squaring both sides,
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