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A wire 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. If both loops carry the same current I in the same direction, the magnetic field at the centre of the double loop will be:

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answer is C.

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Detailed Solution

The radius of the double loop $r = \frac{R}{2}$ . Now,

Magnetic field due to a loop of radius R at the centre of the loop is

$B = \frac{μ_{0} I}{2 R}$

Similarly for the double loop,

$B' = \frac{μ_{0} I}{2 r} = 2 B [∵ r = \frac{R}{2}]$

$B' = 2 B$

Since the currents in the two loops are in the same direction, the net magnetic field at the centre $= 2 B' = 4 B$ .

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