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Q.

A small ring of radius ‘a’ is carrying i, P is a point on its axis at a large distance x from its center. Mathematic induction at P is found to be B1. If the radius is doubled and current is also doubled. Also the distance of P from the center of the ring is doubled. Then find new magnetic induction at P.

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a

2B

b

4B

c

B

d

B/2

answer is C.

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Detailed Solution

The current carrying ring behaves like a short magnetic dipole of dipole moment M = πa2 i.∴BP=μo4π2Mx3Initially B = μ04π2iπa2x3In the second condition B2= μ04π2π(4a2)(2i)(2x)3= μo4π2ia2πx3Thus new magnetic induction = B

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