Infinte number of straight wires each carrying curret I are equally placed as show in the figure. Adjacent wire have currents in opposite direcation. Net magnetic field at point P is :

Options

A. `(mu_(0)I)/(4pi) (In2)/(sqrt(3)a)hatk`
B. `(mu_(0)K)/(4pi)(In4)/(sqrt(3)a)hatk`
C. `(mu_(0)I)/(4pi)(In4)/(sqrt(3)a)(-hatk)`
D. Zero

Answer

B

Explanation

`B_(1)=(mu_(0)I2)/(4 pi a sqrt(3))[sin 30 +sin 30 ](hatk)=(mu_(0)I)/(2piasqrt(3))hatk, B_(2)=(mu_(0)I)/(2pi(2asqrt(3)))(-hatk)`
`B_("Neta")=(mu_(0)I)/(2piasqrt(3))[1-1/2+1/3…….]hatk=(mu_(0)I)/(2piasqrt(3)) In 2 hat k =(mu_(0)I)/(4pi)(In4)/(sqrt(3a))hatk`