Three charges are placed at the corners of three square of side 2m. if the charge 5nc moved from point D too what is the work to be done
Answers
Explanation:
AC=BD=(2)2+(2)2=4+4=22=2.28m
AO=BO=CO=22.828=1.414m
Potential at O, VO=4πε01[AOq1+BOq2+COq3]
Potential at D, VD=4πε01[ADq1+BDq2+CDq3]
W= work done =q[V
Given three charges 5nC, 10nC and −5nC placed at corners A, B and C of square ABCD of side 2m.
To find the work done in transferring 5μC from D to point of intersection of diagonals.
AC=BD=
(2)
2
+(2)
2
=
4+4
=2
2
=2.28m
AO=BO=CO=
2
2.828
=1.414m
Potential at O, V
O
=
4πε
0
1
[
AO
q
1
+
BO
q
2
+
CO
q
3
]
Potential at D, V
D
=
4πε
0
1
[
AD
q
1
+
BD
q
2
+
CD
q
3
]
W= work done =q[V
O
−V
D
]
Here, q=5μC
So, W=5×10
−6
×9×10
9
×[5×10
−9
[
AO
1
−
AD
1
]+10×10
−9
[
BO
1
−
BD
1
]−5×10
−9
[
CO
1
−
CD
1
]]
=45×10
−6
×10
9
×10
−9
[5×(
1.414
1
−
2
1
)+10×(
1.414
1
−
2.828
1
)−5×(
1.414
1
−
2
1
)]
=450×10
−6
×(
1.414
1
−
2.828
1
)
=
1.414
450×10
−6
(1−
2
1
)=159.12×10
−6
Joules