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Potential Difference

Potential Difference :- Potential difference between two points in an electric field is defined as the work done by an external force per unit positive test charge in moving it from one point to another against the electric field without acceleration. It is a scalar quantity and is measured in volts (V).

Let the electric potential at point B be V_B and at point C be V_C, as shown in the diagram :-

By definition of electric potential , the work done per unit positive test charge in moving it from infinity to point C against the electric field is V_C and similarly the work done per unit positive test charge in moving it from infinity to point B against the electric field is V_B (Evidently V_B > V_C) . Therefore, potential difference between points B and C,

$\displaystyle \Delta {{V}_{CB}}=\frac{{{\left( {{W}_{CB}} \right)}_{ext.}}}{{{q}_{o}}}=\frac{{{\left( {{W}_{\infty B}} \right)}_{ext.}}-{{\left( {{W}_{\infty C}} \right)}_{ext.}}}{{{q}_{o}}}=\frac{{{\left( {{W}_{\infty B}} \right)}_{ext.}}}{{{q}_{o}}}-\frac{{{\left( {{W}_{\infty C}} \right)}_{ext.}}}{{{q}_{o}}}$

$\displaystyle \Rightarrow \Delta {{V}_{CB}}={{V}_{B}}-{{V}_{C}}$

Key Conclusions About Potential Difference

(1). V_CB is Positive while moving against the electric field : If we move a unit positive test charge from point C to B (opposite to the direction of the electric field), the potential difference V_CB= V_B – V_C will be is positive.

(2). No Work is done by external force in moving a charge from B to C : Moving a positive charge from B to C requires no external work; the electric field does the work. Hence, the potential difference V_BC= V_C – V_B will be is negative.

(3). Electric Field Direction : The electric field created by a positive charge is directed away from the charge. To bring a positive test charge from infinity to any point in this field, external work is required, which results in a positive potential at any point.

A positive charge gives rise to positive potential.
A negative charge gives rise to negative potential.

(4). Scalar Quantity : Potential difference is a scalar quantity. Its S.I. unit is same as that of electric potential i.e., volt.

(5). Path Independence : The potential difference between two points in an electric field V_CB , does not depend on the path taken from C to B. This is due to the conservative nature of electrostatic fields.

(6). Independent of reference point : Potential difference between two points is independent of reference point.

Potential Difference

Key Conclusions About Potential Difference

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