Question

In the frame work of wires shown in figure, a current I ampere is flowing. Find the magnetic field at O.

Answer 1

Let `hatn` be the unit vector perpendicular to the plane of frame work upwards.
Total magnetic field at P is
`vecB_0=vecB_1+vecB_2+vecB_3+vecB_4`
`=(mu_0)/(4pi)I/r_1(2pi-alpha)(-hatn)+0+(mu_0)/(4pi)I/r_2alpha(-hatn)+0`
`=(mu_0)/(4pi)I((2pi-alpha)/(r_1)+alpha/r_2)(-hatn)`
`B_0=(mu_0)/(4pi)I((2pi-alpha)/(r_1)+alpha/r_2)`
The direction of `vec(B_(0))` is perpendicular to the plane of framework of wire directed inwards.