Q.

Determine the magnetic field at the centre of the current carrying wire arrangement shown in figure. The arrangement extends to infinity. (The wires joining the successive squares are along the line passing through the centre.)

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a

μ0i2πa

b

0

c

22μ0iπaln2

d

none of these

answer is C.

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Detailed Solution

Magnetic field at centre due to a square of side a: B=4μ04πi(a/2)sin45°+sin45°=22μ0iπa For the case in figure Bnet =22μ0iπ1a-12a+13a-14a+… =22μ0iπa1-12+13-14+…=22μ0iπa(ln2)
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Determine the magnetic field at the centre of the current carrying wire arrangement shown in figure. The arrangement extends to infinity. (The wires joining the successive squares are along the line passing through the centre.)