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A wire of length l is bent into a circul...

A wire of length l is bent into a circular loop of radius R and carries a current I. The magnetic field at the centre of the loop is B. The same wire is now bent into a double loop of equal radii. If both loops carry the same current I and it is in the same direction, the magnetic field at the centre of the double loop will be

A

Zero

B

2 B

C

4 B

D

8 B

Text Solution

Verified by Experts

The correct Answer is:
C
Magnetic field at the centre of loop
`B = (mu_(0) I)/(2 R)`
One circular loop
`I = 2pi r implies r = (1)/(2pi)`
`B = (mu_(0)I)/(2l// 2pi) = (mu_(0) pi l)/(l)`
When the bent into two circular loop
`(l)/(2) = 2pi r implies r = (l)/(4pi)`
`B. = (mu_(0) xx 2 xx l)/(2. (l)/(4pi)) = (4mu_(0) lpi)/(l) implies B. = 4B`
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