First slide

Electric field

Question

Three equal charges, each +q, are placed on the corners of an equilateral triangle. The electric field intensity at the centroid of the triangle is

Easy

A

$kq / r^{2}$
B

$3 kq / r^{2}$
C

$\sqrt{3} kq / r^{2}$
D

$z e r o$

Solution

$E_{n e t 1} = 2 E \cos \frac{θ}{2} = 2 E \cos \frac{120}{2} = 2 E \cos 60 = E u p w a r d s E_{n e t 2} = E d o w n w a r d s E_{n e t} = E - E = 0$
Each charge will produce the same magnitude of intensity, say E, at the centroid. These are directed at angles of 120⁰ with each other. So, their vector sum will be zero.

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