A triangle is made from thin insulating rods of different lengths, and the rods are uniformly charged, i.e. the linear charge density on each rod is uniform and the same for all three rods. Then

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The electric field at the incentre of triangle is zero.

If rods are making equilateral triangle of side length 2a ,then field on the axis of triangle passing through centroid and normal to its plane is maximum at distance $\frac{a}{\sqrt{3}}$ from is centroid.

The electric field is zero at the incentre only when it is an equilateral triangle.

If rods are making equilateral triangle of side length 2a ,then field on the axis of triangle passing through centroid and normal to its plane decreases monotonically as distance from centroid increases.

answer is A, B.

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Detailed Solution

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The charge it carries is $Δq = \frac{λrΔφ}{{cos}^{2} φ}$ .where $λ$ is the linear charge density on the rods. The magnitude of the elementary contribution of this small piece to the electric field at the incentre is
$ΔE= \frac{1}{{4πε}_{0}} \frac{{Δqcos}^{2} φ}{r^{2}} = \frac{1}{{4πε}_{0}} \frac{λrΔφ}{r^{2}}$
It can be seen from this result that the same electric field (in both magnitude and direction) would be produced by an arc of the inscribed circle that subtends $Δ ϕ$ at the circle’s centre and carries the same linear charge density $λ$ as the rod.