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Basic Concepts 
Page 2


Basic Concepts 
• Consider an electric field produced by a source 
charge Q at origin. Now we need to calculate the 
amount  of work required to move a test charge q 
from point A to B assuming that it does not affect 
the electric field produced by Q.
• So as we know that electrostatic force is 
conservative, the amount of work done in 
bringing the charge from A to B is change in 
potential energy of the charge at A and B or 
gain in potential energy.
• So ?? ??????
= ?? ?? - ?? ?? .
Q
q
A
B
Page 3


Basic Concepts 
• Consider an electric field produced by a source 
charge Q at origin. Now we need to calculate the 
amount  of work required to move a test charge q 
from point A to B assuming that it does not affect 
the electric field produced by Q.
• So as we know that electrostatic force is 
conservative, the amount of work done in 
bringing the charge from A to B is change in 
potential energy of the charge at A and B or 
gain in potential energy.
• So ?? ??????
= ?? ?? - ?? ?? .
Q
q
A
B
• Now we can assume that the potential energy 
is zero at infinity.
• So, if we assume point A to be at infinity in the 
previous example then, ?? ?????? = ?? ?? - ?? 8
= 
?? ?? .
• So, potential energy of a charge q at any poin
(here, B) is the amount of work done by 
external force in bringing charge q from 
infinity to that point.
Page 4


Basic Concepts 
• Consider an electric field produced by a source 
charge Q at origin. Now we need to calculate the 
amount  of work required to move a test charge q 
from point A to B assuming that it does not affect 
the electric field produced by Q.
• So as we know that electrostatic force is 
conservative, the amount of work done in 
bringing the charge from A to B is change in 
potential energy of the charge at A and B or 
gain in potential energy.
• So ?? ??????
= ?? ?? - ?? ?? .
Q
q
A
B
• Now we can assume that the potential energy 
is zero at infinity.
• So, if we assume point A to be at infinity in the 
previous example then, ?? ?????? = ?? ?? - ?? 8
= 
?? ?? .
• So, potential energy of a charge q at any poin
(here, B) is the amount of work done by 
external force in bringing charge q from 
infinity to that point.
• Now the electrostatic potential at a point, just 
like electric field intensity, is the work done by 
external force in bringing a unit positive 
charge from infinity to that point. It is denoted 
by V.
• So ?? ?? = 
?? ?? q
(from the previous example)
Page 5


Basic Concepts 
• Consider an electric field produced by a source 
charge Q at origin. Now we need to calculate the 
amount  of work required to move a test charge q 
from point A to B assuming that it does not affect 
the electric field produced by Q.
• So as we know that electrostatic force is 
conservative, the amount of work done in 
bringing the charge from A to B is change in 
potential energy of the charge at A and B or 
gain in potential energy.
• So ?? ??????
= ?? ?? - ?? ?? .
Q
q
A
B
• Now we can assume that the potential energy 
is zero at infinity.
• So, if we assume point A to be at infinity in the 
previous example then, ?? ?????? = ?? ?? - ?? 8
= 
?? ?? .
• So, potential energy of a charge q at any poin
(here, B) is the amount of work done by 
external force in bringing charge q from 
infinity to that point.
• Now the electrostatic potential at a point, just 
like electric field intensity, is the work done by 
external force in bringing a unit positive 
charge from infinity to that point. It is denoted 
by V.
• So ?? ?? = 
?? ?? q
(from the previous example)
• Here if we consider a system of charges 
?? 1
,?? 2
,?? 3
??? ?? with their relative position 
vectors ?? 1
,?? 2
,?? 3
??? ?? . Then potential due to 
individual charges would be
?? 1
=
?? 1
4?? ?? 0
?? 1
;?? 2
=
?? 2
4?? ?? 0
?? 2
;?? 3
=
?? 3
4?? ?? 0
?? 3
??? ?? =
?? ?? 4?? ?? 0
?? ?? • Now, according to superposition principle, the net 
potential due to system of charges ?? =
1
4?? ?? 0
 
?? 1
?? 1
+
P
?? ?? ?? ?? ?? ?? ?? ?? ?? ??
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