explain potential due to point charge electric potential for Jessica Roshini from 12th 3mark
Answers
Answer:
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Explanation:
The electrostatic potential at any point in an electrostatic field is defined as the work done in carrying a unit positive charge from infinity to that point against the electrostatic force of the field.
Consider a point Charge +Q at O.
Let P be a point at a distance r from O.
Consider a point A at a distance x from O.
The magnitude of electrostatic force on unit-positive charge at A, is
F=
4πε
0
1
x
2
Q×i
F=
4πε
0
x
2
Q
along OP
Work Done in moving a unit positive charge from A to B through a small distance dx is,
ΔW=
F
.d
x
=Fdxcos180
o
ΔW=−Fdx
ΔW=
4πε
0
x
2
−Q
dx
Total work done in moving a unit positive change from infinity to the point P is,
W=∫
∞
r
4πε
0
−1
x
2
Q
dx=−
4πε
0
x
2
Q
∫
∞
r
x
2
1
dx
W=−
4πε
0
Q
[
x
1
]
∞
r
=
4πε
0
Q
[
r
1
−
∞
1
]
W=
4πε
0
r
Q
By definition, this work done is equal to the electrostatic potential (V) at that point due to Q.
V=
4πε
0
1
r
Q