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.

Question

Infinity Learn · Accepted Answer

The current carrying ring behaves like a short magnetic dipole of dipole moment M $$=$$ π$$a2$$ i.∴$$BP=$$μ$$o4$$$$π$$$$2Mx3Initially$$ B $$=$$ μ$$04$$$$π$$$$2i$$$$π$$$$a2x3In$$ the second condition $$B2=$$ μ$$04$$$$π$$$$2$$π$$(4a2)(2i)(2x)3=$$ μ$$o4$$$$π$$$$2ia2$$$$π$$$$x3Thus$$ new magnetic induction $$=$$ B

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