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Q.

Determine the magnitude of magnetic field at the centre of the current carrying wire arrangement shown in the 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

$\frac{μ_{0} i}{\sqrt{2} πa}$

b

none of these

c

$\frac{2 \sqrt{2} μ_{0} i}{πa} \ln 2$

d

0

answer is C.

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Detailed Solution

$A t t h e c e n t r e B_{R e s u l \tan t} = \frac{2 \sqrt{2} μ_{0} i}{πa} - \frac{2 \sqrt{2} μ_{0} i}{π (2 a)} + \frac{2 \sqrt{2} μ_{0} i}{π (3 a)} - . . . . . . . . . = \frac{2 \sqrt{2} μ_{0} i}{πa} (1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + . . . . . . . . .) = \frac{2 \sqrt{2} μ_{0} i}{πa} \ln 2$

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