There are two infinite long parallel straight current carrying wires, A and B separated by a distance r. Figure. The current in each wire is I. The ratio of magnitude of magnetic field at point P and Q when points P and Q lie in the plane of wires is:

Answer

`(8)`

Explanation

Magnetic field at P due to currents in two wires will be acting perpendicular to the plane of wires, upwards and is given by
`B_P=(mu_0)/(4pi)(2I)/((r//2))+(mu_0)/(4pi)(2I)/((r//2))=(2mu_0I)/(pir)`
Magnetic field at Q due to current in A is perpendicular to the plane of wire upwards and due to current in B is perpendicular to the plane of wire downwards and is given by
`B_Q=-(mu_02I)/(4pi2r)+(mu_02I)/(4pir)=(mu_0I)/(4pir)`
`:. B_P/B_Q=((2mu_0I//pir))/((mu_0I//4pir))=8`