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Q.

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


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a

Question Image

b

Question Image

c

Question Image

d

Question Image 

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,
Question ImageWhere 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
 Question ImageLet us now examine the question. The value of magnetic induction at a distance is given as
 Question Image for the same coil's value at the centre, we must determine the distance.
Allow the distance to be Question ImageNow, using (1)
For magnetic induction at the centre, Question Image. Putting this in (1) , we get,
Question Imagewhere Question Image (centre) is the value of the magnetic induction at the centre.
Using (1) , magnetic induction at the distance Question Image on the axis is given by,
Question ImageNow, by the problem Question Image Question ImageTherefore, putting Question Image and (3) in (4) , we get,
Question ImageQuestion ImagePutting cube root on both sides
Question ImageSquaring both sides,
Question ImageQuestion ImageQuestion ImagePutting square root on both sides,
Question ImageHence, the required distance is Question Image. Therefore, the correct option is (2) Question Image.
Hence, option 2 is the correct answer.
 
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