Two insulating infinite long conductors carrying currents `I_1(=2A)` and `I_2(=4A)` lie mutually perpendicular to each other in the same plane, as shown in figure. Find the magnetic field at the point P(a,b), where `a=4cm`, , `b=3cm`.

Answer

`1*66xx10^-5T`; normally outwards

Explanation

Magnetic field at P due to current `I_1` is
`B_1=(mu_0)/(4pi)(2I_1)/(a)`, directed normally inwards
Magnetic field at P due to current `I_2` is
`B_2=(mu_0)/(4pi)(2I_2)/(b)`, directed normally outwards
Net magnetic field at point P is
`B=B_2-B_1`, directed normally outwards.
`=(mu_0)/(4pi)2[I_2/b-I_1/a]`
`=10^-7xx2[(4)/(3xx10^-2)-(2)/(4xx10^-2)]`
`=1*66xx10^-5T`