The electric field at a point A on the perpendicular bisector of a uniformly charged wire of length λ = 3m and total charge q = 5 nC is x V/m. The distance of A from the center of the wire is b= 2m. Find the value of x.
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Sol. Let a rod of length λ and charge q and a point A are as shown in figure (at distance = b). Charge per unit length = 
. Let a small component dy along the rod at distance y from center of rod is considered.
charge on the element dy = 
dy
∴ Electric field at point A due to this charge ⇒ dE = 
Now, x component of dE = dE cos θ = 
and y component of dE = – dE sin θ = – 
Now, electric field due to total length of rod = 
= 
= 
= 
= 
(along x axis)
and 
= – 
= 0
So, net electric field is along x–axis and is equal to 
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