Three negatively charged spheres, each with a charge of , are fixed at the vertices of an equilateral triangle whose sides are 20 cm long. Calculate the magnitude of the total electric force on each sphere.
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Answer:
As shown in figure draw AD⊥BC
∴AD=ABcos30
o
=
2
l
3
Distance AO of the centroid O from A
=
3
2
AD=
3
2l
2
3
=
3
1
∴ Force on Q at O due to charge q
1
=q at A
F
1
=
4πε
0
1
(l
3
)
2
=
4πε
0
l
2
3Qq
,along AO
Similarly, force on O due to charge q
2
=q at B
F
2
=
4πε
0
l
2
3Qq
, along BO
and force on Q due to charge q
3
=q at C
F
3
=
4πε
0
l
2
3Qq
along CO
Angle between forces F
2
and F
3
=120
o
By parallelogram law, resultant of
F
2
and
F
3
4πε
0
l
2
3Qq
along OA
∴ force on Q=
4πε
0
l
2
3Qq
−
4πε
0
l
2
3Qq
=0
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