Question

A current carrying wire is placed in the grooves of an insulating semi circular disc of radius r as shown the current enters at point a and leaves from point b determine the magnetic field at point d

Answer 1

magnetic field due to a circular loop at its center is given by

$B = \frac{\mu_o i }{2r}$

here

r = radius of the disc

i = current in the wire

now if we used semicircular loop

then the magnetic field at the center of the loop will be half that of initial value

$B' = \frac{B}{2}$

so the magnetic field at point d is given by

$B' = \frac{\mu_o i}{4r}$

so above is the magnetic field required at that point