Calculate the magnetic field at a point p which is perpendicular bisector to current carrying straight wire
Answers
the magnetic field at a point p which is perpendicular bisector to current carrying straight wire is given as follow
1-Lets draw a diagram AB is a line segment of particular length. The point O represents the centre of the line segment AB.
2-PN is the line passing through O such that it (1) intersects a given segment at a 90° angle, and (2) passes through the given segments midpoint.
3-Thus, a perpendicular bisector is a special kind of segment, ray, or line which intersects the given segment at 900 and passes through the given segments midpoint. Since, it makes 900, it is also called as right bisector.
4-We know that the magnetic field due to a straight current carrying conductor is given by
μ0I / 4∏R [ sin Ɵ1 + sin Ɵ2 ]
AOB is the current carrying conductor. P is a point such that a perpendicular bisector is drawn passing through this point with the current carrying conductor AB.
sin Ɵ = opposite side/ Hypotenuse = L/2 Divided by √[R2 + (L/2)2] = L/2 divided by 1/2√[4R2 + L2] = L /√[4R2 + L2]
Hence, from the general expression, B = μ0I / 4∏R [ sin Ɵ1 + sin Ɵ2 ]
μ0I / 4∏R [ sin Ɵ - sin (-Ɵ) ] = μ0I / 2∏R sin Ɵ
B = μ0I / 2∏R sin Ɵ
Substituting for sin Ф, we get, B = μ0I L / 2∏R√[4R2 + L2]