Potential Difference

Potential Difference

AU : May-07

• In the last sections it has been discussed that the work done in moving a point charge Q from point B to A in the electric field    is given by,

• If the charge Q is selected as unit test charge then from the above equation we get the work done in moving unit charge from B to A in the field   . This work done in moving unit charge from point B to A in the field    is called potential difference between the points B and A. It is denoted by V.

Potential difference =     ... (4.4.2)

• Thus work done per unit charge in moving unit charge from B to A in the field    is called potential difference between the points B and A.

• Notation : If B is the initial point and A is the final point then the potential difference is denoted as VAB which indicates the potential difference between the points A and B and unit charge is moved from B to A.

Key Point : V_AB positive if the work is done by the external source in moving the unit charge from B to A, against the direction of    .

• The work done in moving unit test charge from infinity to a point in an electric field is called an electric potential of that point.

1. Unit of Potential Difference

• The potential difference is work done per unit charge. The work done is measured in joules while the charge in coulombs. Hence unit of potential difference is joules/coulombs (J/C). But practically the emit is called Volt (V).

One volt potential difference is one joule of work done in moving unit charge from one point to other in the field   

1 volt = 1 joule / 1 coulomb … (4.4.4)

Ex. 4.4.1 Given field intensity  calculate the potential difference between two points P(l, -1, 0) and Q(2, 1, 3).

AU : May-07, Marks 10

Sol.: 

As integral does not depend on the path from Q to P we can divide the path as,

Path 1 Q(2, 1, 3) to (1, 1, 3) …. Only x varies

Path 2 (1, 1, 3) to (1, -1, 3) …. Only y varies

Path 3 (1, -1, 3) to P(l, -1, 0) …. Only z varies

Review Question

1. Explain the concept of electric potential difference.