Two parallel wire carrying equal currents in opposite directions are placed at `x=+-a` parralel to y-axis with `z=0`. Magnetic field at origin O is `B_1` and at `P(2a,0,0) is B_2`. Then, the ratio `B_1//B_2` is

Options

A. `-3`
B. `-1/2`
C. `-1/3`
D. `2`

Answer

A

Explanation

Case I: if the currents are in the directions shown in figure. Then

`vec(B)_(1)=-2((mu_(0)i)/(2pia))hatk=-(mu_(0)i)/(pia) hatk`=magnetic field at `O`
`vec(B)_(2)=(mu_(0)i)/(2pia)hatk-(mu_(0))/(2pi) (1)/(3a) hatk` = magnetic field at `P`
`=(mu_(0))/(3pi) (i/a)hatk`
`:. B_(1)//B_(2)=-3`
Case II: In this case
`vec(B)_(1)=(mu_(0)i)/(pia) hatk`
and `vec(B)_(2)=(mu_(0)i)/(3pia) (i/a) hatk`
`:. (B_(1))/(B_(2))=-3`