In the net work shown in figure,find the magnetic field at the centre O of the coil.

Answer

`2xx10^-5T` normally out of the plane of paper

Explanation

Here, `I_1=I_2=I/2=5/2A`, `Ob=r=5xx10^-2m`
Total magnetic field induction at O due to current in the net work is
`vecB=vecB_(ab)+vecB_(bcd)+vecB_(bed)+vecB_(df)`
`=(mu_0)/(4pi)I/rhatn+(mu_0)/(4pi)(piI)/(r)hatn+(mu_0)/(4pi)(piI)/(r)(-hatn)+(mu_0)/(4pi)I/rhatn`
where `hatn` is a unit vector normally out of the plane of paper.
`:. vecB=2xx(mu_0)/(4pi)I/rhatn=2xx10^-7xx(5)/(5xx10^-2)hatn`
`=2xx10^-5`, normally out of the plane of paper.