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A long straight wire, carrying I is bent...

A long straight wire, carrying I is bent at its mid-point to form an angle of `45^@)`. Induction of magnetic field ( in tesla) at point P, distant R from point of bending is equal to

Text Solution

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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)
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