Question

A long straight wire, carrying current I, is bent at its midpoint to form an angle of `45^@`. Find the induction of magnetic field at point P, distant R from the point of bending (as shown in)

Answer 1

Since point P lies on axis of
straight part ab, therefore , magnetic induction due to this part is
equal to zero.
For part bc: From fig
`r=Rcos 45^@`.
Since both the ends b and c are
on the same side of normal PN,
therefore, `alpha` is negative and `beta` is positive.
Hence, `alpha=-45^@ and beta=+90^@`.
Using `B=(mu_0I)/(4pir)(sin alpha+sin beta)`, we have `B=((sqrt2-1)mu_0I)/(4piR)`
(into the plane of paper)