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MAMS ACADEMY FOR CAREER EXCELLENCE 

RIYADH, SAUDI ARABI A  

PHYSICS NOTES: Electric Potential, Potential Energy and Dipole Date: March 18, 2

ES3

Electric Potential: The effect of charge in its surrounding environment can also be represented by usinganother physical quantity known as Electric Potential other than Electric Field. One difference is that Fielda vector quantity and Potential is scalar quantity. For field direction is required but for potential no directio

only magnitude is required.

Potential due to point charge: Consider a point charge placed at some point in a material medium. The

potential due to that point charge at point P at some distance r from it is given by.1

4 o r 

q

r πε ε 

= ×V  , rememb

here q is to be used with sign. For positive charge this quantity is positive but for negative charge it isnegative

.

Potential Difference: Due to point charge potential is different at different point because it varies with

distance as1

V r 

∝ . So when we move from one point to another point in an electric field of that point charg

we will get difference of potential Also known as potential difference.

As we move away from the positive point charge the magnitude of the field decreases that means if wemove a positive small test charge away from that point charge the magnitude of the force experience by idue to field, decreases. Direction of force on test charge always points away from the positive charge. If

displacement is also away from it (moving away from point charge). So Work done by the field on the testcharge is positive.Let’s consider we move from point A to point B in an electric field. Then Potential difference between thespoints is written as VA-VB is defined as work done by the electric field on the test charge when it is movedrom A to B divided by that test charge. External work done on the test charge in moving it from A to B wilbe negative of the work done by the electric field.

 fieldA B

 A B

o

W V V 

q

→− = externalA B A B

o

W 

q

→−− =V V  OR externalA B

 B A

o

W V V 

q

→− = , its very easy to remember.OR

f test charge is taken from infinity to a point at distance r from point charge and as potential at infinity is zbecause the effect of charge at infinity vanishes, so (work done in moving test charge divided by testcharge) from infinity to that point will give potential at that point.

ex te rn al B B B

o

W V V V 

q

∞→∞− = = This is also definition of potential at a point.

Note: Field is defined using force as force per unit test charge, potential is defined using work done as wodone per unit test charge. AND this work is conservative i.e. independent of the path followed.

Potential Energy of electric charges in electric field: Consider there are two point charges placed in amedium at separation r between each other. If these are released from that position then they will accelerand move away from each other gaining KE. So, before release they must have potential energy stored inboth charges. So, PE must be stored in a system of charges. If there are three point charges placed inmedium. Then PE is due to all three charges as a system.

8/2/2019 Electric Potential ,Potential Energy, Dipole Notes 3

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Derivation Consider two point charges and . If is brought from infinity towards to final distance

rom . This work will be negative of the work done in taking from initial distance r to final distance of

1q

2q

2q

1q

1q

2q ∞

Let’s find this second work.

Work Done by field of in doing so is1

q 1 2

2

0

W 

r 

q qdw K dr  

r 

∞ ×⎛ ⎞= ⎜ ⎟

⎝ ⎠∫ ∫ or 1 2

0

W 

r 

Kq qdw

r 

∞−⎡ ⎤

= ⎢ ⎥⎣ ⎦∫ or

1 2 1 20Kq q Kq q

W r 

− −⎛ ⎞ ⎛ ⎞− = −⎜ ⎟ ⎜ ⎟∞⎝ ⎠ ⎝ ⎠

or 1 2Kq q

W r 

= Hence work done in moving from infinity to final distance r w

be

2q

1 2Kq q

r − This is conservative work done . Now Change in potential energy of conservative force is rela

o the work done by the conservative force asconservative

U W ∆ = − or 1 2

r 

Kq q

r 

∞

⎛ ⎞− = − −⎜ ⎟

⎝ ⎠

U U  hence 1 2

r 

Kq qU 

r 

= .

Remember to put charges with sign as in potential formula

Potential Energy of the system of charges: Consider three charges placed in space as shown in the figur

The expression for potential energy of system is

2 3 3 11 2

1 2

Kq q Kq qKq q

3r r r 

= + +U   

similarly we can find PE of system of any number

of point charges placed in medium.

Electric Dipole: It is a system of two equal and opposite point charges separated by some distance rbetween each other. Remember if there are number of point charges in a medium then number of dipolehere is equal to the number of pairs of equal and opposite point charges.

Electric Dipole Moment of Dipole: It is a physical quantity that describes electric dipole. It is a vector quan

denoted by

whose direction is always from –ve charge to positive charge in dipole. Its magnitude =chamagnitude x separation r) , SI unit is Nm Dimensional Formula [L

P

P q r = × 1A1T1]

Note : Field, Force and dipole moment are vector, potential and potential energy are scalar quantities. Alsor derivations involving dipole we take the separation between charge as r=2a for making derivationssimple.

,,,,,,,,,,,,,Have a Nice Day…………