. Find the electric potential acting at A point of square ABCD, of side 2 m. Charges present on corners B,C and D are 1C, -1C and -1C
Answers
Answer:
ABCD is a square of side 0.2 m. Charges of 2×10
−9
,4×10
−9
,8×10
−9
coulomb are placed at the corners A, B and C respectively. Calculate the work required to transfer a charge of 2×10
−9
coulomb from corner D to the centre of the square.
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Answer
AC=BD=
(0.2)
2
+(0.2)
2
=
2
×0.2=0.28m
∴AO=BO=CO=
2
0.28m
=0.14m
V i.e, Potential at O;V
o =
4πε
01[
AO
q
1 +
BO
q
2 +
CO
q
3 ]
V i.e, Potential at D;V
D =
4πε
01 [
AD
q
1 +
BD
q
2 +
CD
q
3 ]Work done =q[V
o
−V
D
]
=
4πε
0
2×10
−9[
0.14
2×10
−9 +
0.14
4×10
−9 +
0.14
8×10
−9 −
0.2
2×10
−9−
0.28
4×10 −
0.2
8×10
−9 ]
On solving, we get
W=2×10
−9
×2×10
9
[
0.14
14×10
−9
−
0.2
10×10
−9
−
0.28
4×10
−9
]
=4×[10
−7
−0.5×10
−7
−0.14×10
−7
]
=5.40×10
−7
Joules.
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