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

Options

A. `(mu_(0)i)/(sqrt(2)pia)`
B. `0`
C. `(2sqrt(2)mu_(0)i)/(pia) ln 2`
D. None of these

Answer

C

Explanation

Magnetic field at centre due to a square of side `a:`
`B=4[(mu_(0))/(4pi) i/((a//2))[sin 45^(@)+sin45^(@)]] =(2sqrt(2) mu_(0)i)/(pia)`
For the case in fig.
`B_("net")=(2sqrt(2) mu_(0)i)/(pi)[1/a-1/(2a)+1/(3a)-1/(4a)+.....]`
`=(2sqrt(2)mu_(0)i)/(pia)[1-1/2+1/3-1/4+.....]`
`=(2sqrt(2)mu_(0)i)/(pia)(ln 2)`