Three charges +q each are placed at three vertices of an equilateral triangle
of side length a each. Then net electrostatic potential at the centroid of the
triangle is
(a)0
(b)3 sqrt{3} q/4πε0
(c)6q/4πε0a
(d)3q/2πε0a
Answers
Answer:
3 point charges of +Q are placed on an equilateral triangle. They will repel each other and go away from each other and go away from each other. So, the charge which we want to keep in the center should be negatively charged.
Let us consider the charge at center be −q. Let the length of side of equilateral triangle is a. Consider an equilateral triangle ABC, with centroid at D.
F
1
=
a
2
kQ
2
along
AB
F
2
=
a
2
kQ
2
along
CB
F
3
=
a
2
3kQq
along
BD
in horizontal direction, for equilibrium.
F
1
cos60
∘
+F
2
=F
3
cos30
∘
⇒
a
2
kQ
2
×
2
1
+
a
2
kQ
2
=
a
2
kQq
×
2
3
⇒
2a
2
3kQ
2
=
a
2
2
3kQq
3
⇒q=
3
Q
Since q is negatively charged,
So, q=
3
−Q
Explanation: