A straight metal wire of length L is carrying a current i.
Calculate the magnetic field intensity due to this wire at a point which is at the same distance from both ends of the rod and equal to length of road.

Explanation

Point A is at a distance from the wire as shown in figure. Since ` MO = l//2 " and " MA = l, angleMAO = alpha_(1) = 30^(@)` .
Similarly , ` angleNAO = alpha_(2) = 30^(@)`
Let us consider the triangle ` DeltaAOM` .
` cos 30^(@) = x/l `
` x = l cos 30^(@) = (l sqrt3)/2` Megnetic field at point A
` B_(A) = (mu_(0)i)/(4pi x) [sin alpha_(1) + sin alpha_(2)]`
` = (mu_(0)i)/(4pix) [sin 30^(@) + sin 30^(@)]`
` = (mu_(0)i)/(4pix) xx 2 xx 1/2`
` = (mu_(0)i)/(4 pi x) `
` B_(A) = (mu_(0)i)/(4 pi xx ((lsqrt3)/2))`
` = 2/sqrt3 xx 10^(-7) (i/l) T`