Potential Difference

Concept Explanation

Potential Difference

Electric Potential:

Electric potential at a point in electric field is defined to be equal to the minimum work done by an external agent in moving a unit positive charge from infinity or a reference point to that point against the electrical force of the field. If W is the work done by external agent in bringing a positive test charge q_o from infinity to a point then the potential V at that point,

$large V=frac{W_{ext}}{q_{0}}$

According to Newtons Third Law of motion i.e. for every action there is equal and opposite reaction

The work done by an external agent in bringing a positive test charge q_o from infinity to a point will be equal and opposite ti the work done by the electric field on a positive test charge q_{o, if}

$W_{E}=work;done;by;electric field$

$W_{E}= -W_{Ext}$

$V=-frac{W_{E}}{q_{0}}$

The SI unit of electric potential is joule/coulomb or volt.

Potential Difference: Potential difference between two points is equal to the minimum work done in moving a unit positive test charge from one point to the other.

$V_{B}-V_{A}=frac{W_{AB}}{q_{0}}Rightarrow W_{AB}=q_{0}(V_{B}-V_{A})$ ,

$W_{E}$ is the work done by the electric field then

$W_{AB.}=-W_{E}$

$W_{E.}=-W_{AB}= -q_0(V_B-V_A)$

$W_{E.}=q_0(V_A-V_B)$

Hence the work done by external agent

$W_{AB}=q_{0}(V_{B}-V_{A})$

And Work done by the electric field is

$W_{E.}=q_0(V_A-V_B)$

We know that heat energy flows from the higher temperature to the lower temperature, and this process stops when the both are at the same temperature. Same is the case with electricity, when the ends of an electrical conductor are at different potentials or we can say that when there is a potential difference - charge in the conductor flow from the higher potential to the lower potential.The flow of charge persists until both ends reach the same potential. Without a potential difference, no flow of charge will take place.

Illustration: How much work is done in moving a charge of 2 C from a point of 118 V to a point at 128 V ?

Solution: Given, charge, q = 2 C

Potential at point A

$V_{A}=118;V$

and Potential at point B

$V_{B}=128;V$

Work done, W = ? We know that,

Potential difference,

$Delta V=V_{B}-V_{A}$ $=128-118=10V$

$large therefore$ Work Done,

$W_{AB}=q_{0}(V_{B}-V_{A})$

$W_{AB}=q_{0};Delta V$

$W=Delta Vtimes q=10times2=20 J$

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Sample Questions

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Question : 1

Electric potential is _____________.
A. A scalar quantity	B. A vector quantity	C. Neither scalar nor vector	D. Sometimes scalar and sometimes vector
Right Option : A
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Question : 2

When the ends of a metal wire are not connected to a battery
A. Electrons move from positive electrode to negative to a battery	B. Electrons move from negative electrode to positive electrode	C. electrons move in random directions	D. Protons omve inrandom direction in such a way that their net movement in a unit volume is zero
Right Option : C
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Question : 3

Choose the correct statement. A In case of an electric cell chemical energy is converted into electrical energy. B The current flows when there is potential difference
A. Only A is true	B. Only B is true	C. Both A and B are true	D. Both A and B are false
Right Option : C
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