Three point charges of +2 uC , -3uC , and -3uC are kept at the vertices A,B and C respectively of an equilateral triangle of side 20 cm as shown in the figure(attached with question).What should be the sign and magnitude of the charge to be placed at the midpoint M of the side BC so that the charge at A remain in equilibruium.
Answers
Explanation:
The charge at any vertex will remain in equilibrium if the net force experienced by this charge due to all other three charges is zero.
Let Q be the required charge to be kept at the centroid G.
Considering the charge at A,
Force
F
1
on charge at A due to charge at B
F
1
=
4πϵ
0
1
a
2
q
2
along
BA
Force
F
2
on charge at A due to charge at C
F
2
=
4πϵ
0
1
a
2
q
2
along
CA
Since angle between
F
1
and
F
2
is 60
∘
.
F
1
+
F
2
=
3
4πϵ
0
1
a
2
q
2
along
GA
Also, the distance of centroid G from any vertex is
3
a
The nature of charge to be kept at G has to be opposite (−ve) so that it exerts a force of attraction on charge (+q) kept at A to balance the force
F
1
+
F
2
Force exerted by (−Q) kept at G on charge (+q) at A=
4πϵ
0
1
(
3
a
)
2
=
4πϵ
0
1
a
2
Q.3q
along
AG
Equating the two forces, being equal and opposite.
3
4πϵ
0
1
a
2
q
2
=−
4πϵ
0
1
a
2
3Qq
⇒Q=−
3
q
.
