cos F cos x y q q q q q r F F F F F F The charges q and q are equi- distant from q . As a result the strengths (magnitude) of the forces F and F are the same even though their directions are different. Therefore the vectors representing these two forces are drawn with equal lengths. But the charge q is located farther compared to q and q .
Since the strength of the electrostatic force decreases as distance increases, the strength of the force F is lesser than that of forces F and F . Hence the vector representing the force F is drawn with smaller length compared to that for forces F and F . From the figure, r and The magnitudes of the forces are given by kq = × Without the superposition principle, Coulomb’s law will be incomplete when applied to more than two charges. Both the superposition principle and Coulomb’s law form fundamental principles of electrostatics and explain all the phenomena in electrostatics.
But they are not derivable from each other. Note EXAMPLE . Consider four equal charges q , q , q and q = q = + μC located at four different points on a circle of radius 1m, as shown in the figure. Calculate the total force acting on the charge q due to all the other charges.
x y q q q q Solution According to the superposition principle, the total electrostatic force on charge q is the vector sum of the forces due to the other charges, tot The following diagram shows the direction of each force on the charge q . 12th - 12th - - - - - Unit Electrostatics . ELECTRIC FIELD AND ELECTRIC FIELD