Given an equilateral triangle with side L, find E at its centroid. The linear charge density is as shown in figure.

Explanation

The electric field strength due to the three rods AB, BC and CA are shown in figure.

`barE_(AC) =(3lambda)/(2pi in_(0)L)` (towards B)
`barE_(AB) =(3lambda)/( 2pi in_(0)L)` (towards C)
`barE_(BC)=(3lambda)/(2pi in_(0)L)` (towards midpoint of BC)
`barE_("Net") = barE_(AC) +barE_(AB) +barE_(BC)`
`=(3lambda)/(pi in_(0)L)` (towards midpoint of BC)