Question -
Answer -
Take a long thin wire XY(as shown in the figure) of uniform linear charge density
Consider a point A at aperpendicular distance l from the mid-point O of the wire, asshown in the following figure.
Let E bethe electric field at point A due to the wire, XY.
Consider a small lengthelement dx on the wire section with OZ = x
Let q bethe charge on this piece.
Electric field due to thepiece,
The electric field isresolved into two rectangular components. 
is the perpendicularcomponent and 
is the parallel component.
When the whole wire isconsidered, the component is cancelled.
Only the perpendicularcomponent affects point A.
Hence,effective electric field at point A due to the element dx is dE1.
On differentiating equation (2), we obtain
From equation (2),
Putting equations (3) and(4) in equation (1), we obtain
The wire is so long that 
tends from 
to 
By integrating equation(5), we obtain the value of field E1 as,
Therefore, the electric field due to long wire is 