A long straight wire, carrying current I , is bent on its midpoint to form an angle of 45 degrees - Science - Magnetic Effects of Electric Current

Question

A long straight wire, carrying current I , is bent on its midpoint
to form an angle of 45 degrees Find the induction of magnetic field
at point P, distant R from the point of bending

Vaibhav T. · Accepted Answer

Dear Student,

Since the point P lies on the axis of straight part OA, magnetic field at point P is zerodue to a part OA of wire
For part OC, from ∆OPN,d=R cos45°Since both the ends O and C are on the same side of the normal PN, therefore,ϕ1=-45° and ϕ2=90°So, B=μ0i4πdsin ϕ1+sin ϕ2⇒ B=μ0i4πR cos45°sin-45°+sin90°⇒ B=μ0i×24πR-sin45°+1⇒ B=2μ0i4πR1-12⇒ B=2μ0i4πR2-12⇒ B=μ0i4πR2-1

A long straight wire, carrying current I , is bent on its midpoint to form an angle of 45 degrees . Find the induction of magnetic field at point P, distant R from the point of bending