The loop shown in figure in carrying a current I the magnetic induction at the common centre O of the semi circles is B.
Now the wire of the loop is bent to form a circular ring which is carrying the same current I. Then magnetic induction at the centre of the ring will be

Question

The loop shown in figure in carrying a current I the magnetic induction at the common centre O of the semi circles is B.

Now the wire of the loop is bent to form a circular ring which is carrying the same current I. Then magnetic induction at the centre of the ring will be

Infinity Learn · Accepted Answer

$$B=$$μ$$0I4R+$$μ$$0I4(R2)=3$$μ$$0I4RIf$$ radius of the circular ring be $$R1$$, then $$2$$$$π$$$$R1=$$π$$R+$$π(R2)+R$$⇒$$R1=3$$$$π$$$$R2$$×$$2$$π$$+R2$$π$$=(3$$π$$+24$$π$$)R$$∴ $$B1=$$μ$$0I2R1=$$μ$$0IR(3$$π$$+2)/2$$π$$=$$μ$$0I$$×$$2$$$$π$$$$R(3$$π$$+2)⇒$$B1=2$$π(3$$π$$+2)×$$4B3=8$$$$π$$$$B3(3$$π$$+2)$$

The loop shown in figure in carrying a current I the magnetic induction at the common centre O of the semi circles is B.
Now the wire of the loop is bent to form a circular ring which is carrying the same current I. Then magnetic induction at the centre of the ring will be

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