Potential difference and emf

 

POTENTIAL DIFFERENCE:

When the ends of a conducting wire are connected to the terminals of a battery, an electric field is setup throughout the conductor. This field exerts a force on the charge (electron). Let Fe be the force exerted by the electric field on a free charge q. The free charges accelerate in the direction of the electric field (If the free charges are electrons, then the direction of electric force on them is opposite to the direction of electric field). It means the electric field does some work to move free charges in a specified direction.

                              

Let the electric force made the charges move through a distance ‘l’ from A to B as shown in figure . We know that, the work is the product of force and distance along the direction of force.

Hence, work done by the electric force on a free charge q is given by

W = Fe l   [since work is the product of force and displacement]

Work done by the electric force on unit charge = W/q = Fe l/q

“Work done by the electric force on unit positive charge to move it through a distance ‘l’ from A to B” is called potential difference between those points. Potential difference is denoted by a symbol V. The potential difference between two points separated by a distance l in a conducting wire is given by,

V = W/q = Fe l/q

This potential difference is also called voltage. The SI unit of potential difference is “Volt” and it is denoted by V.

1 Volt = 1 Joule/1 Coulomb

1V = 1J/C

ELECTRO MOTIVE FORCE (E.M.F):

E.M.F is similar concept to potential difference. But both are different. Potential difference is generated by the work done by electric force between the two ends of a conductor where as E.M.F is generated by the work done by chemical force between the two terminals of a battery.

 

E.M.F can be defined as “work done by chemical force in moving unit positive charge from one terminal to another terminal of a battery”.

E.M.F can be denoted with ‘V’ or ‘Ɛ’ (epslon)

V=W/q

let d be the distance between the two terminals of a battery.

Then V=W/q=Fed/q    [since work is the product of force and displacement]

S.I unit of E.M.F is volt

1 volt=joule/coloumb

So formula and units are same for potential difference and E.M.F

You might get one doubt while reading the concepts of potential difference and E.M.F. We learned that positive charges (lattice ions) are fixed in their places in solid conductors according to Lorentz and Drude theory. But in these concepts we are saying that work done on unit positive charge.

How is this possible?

  we can observe the motion of positive as well as negative ions to their respective plates in case of liquids, for example in the process of electrolysis.

So, in solids also we take convention that when a negative charge is moved from A to B, then a positive charge is assumed to be moved from B to A. 

Like this we assume the motion of positive charges conventionally.

Important: In a closed circuit, electrons will move from negative terminal to positive terminal of a battery externally. Protons are assumed to be moving from positive to negative terminal of a battery externally (direction of conventional current).