The wire shown in figure carries a current of `10A`. Determine the magnitude of the magnetic field at the centre O.
Given radius of the bent coil is `3cm`.

Explanation

Let `hatn` be the unit vector perpendicular to the plane of wire loop directed outwards.
Here, `I=10A`, `r=3cm=3xx10^-2m`. Angle subtended by circular arc at O, `theta=270^@=(3pi//2)rad`. Magnetic field at O is
`vecB_0=vecB_(ab)+vecB_(bcd)+vecB_(de)=0+(mu_0)/(4pi)I/rtheta(-hatn)+0`
`vecB_(ab)` and `vecB_(de)` are zero because point O lies on the wires `ab` and `de`.
`:. B_0=(mu_0)/(4pi)xxI/rtheta=10^-7xx(10)/(3xx10^-2)xx3/2pi`
`=1*57xx10^-4T`
It is acting perpendicular to the plane of circular arc directed downwards.