Three long wires, each carrying current `i` are placed parallel to each other. The distance between `I` and `II` is `3d`, between `II` and `III` is `4d` and between `III` and `I` is `5d`. Magnetic field at site of wire `II`

Options

A. `(5mu_(0)i)/(24pid)`
B. `(10mu_(0)i)/(24pid)`
C. `(15 mu_(0)i)/(24 pid)`
D. `(20 mu_(0)i)/(24 pid)`

Answer

A

Explanation

At the wire `(II)`
Magnetic field due to `I, B_(1)=(mu_(0)i)/(2pi.3d)`
Magnetic field due to `III, B_(2)=(mu_(0)i)/(2pi.4d)`
`B_(1)` and `B_(2)` are perpendicular
Resulatant magnetic field
`B_(R)=sqrt(B_(1)^(2)+B_(2)^(2))=(mu_(0)i)/(2pid)sqrt(1/(3^(2))+1/(4^(2)))`
`=(mu_(0)i)/(2pid)sqrt((4^(2)+3^(2))/(3^(2).4^(2)))=(5mu_(0)i)/(2pidxx12)=(5mu_(0)i)/(24 pid)`