force between these two particles is given by ke e = = = × = . × – N hanged vertically. Since they are positively charged spheres, there will be a repulsive force between them and they will be at equilibrium with each other at an angle of ° with the vertical. At equilibrium, each charge experiences zero net force in each direction.
We can draw a free body diagram for one of the charged spheres and apply Newton’s second law for both vertical and horizontal directions. The free body diagram is shown below. mg F e T sinθ T cosθ θ θ x y In the x -direction, the acceleration of the charged sphere is zero. Using Newton’s second law ma tot = ) , we have T F i e sin θ = T F e sin θ = ( ) Here T is the tension acting on the charge due to the string and F e is the electrostatic force between the two charges.
In the y -direction also, the net acceleration experienced by the charge is zero. T j mg j cos θ = T mg cos θ = . ( ) By dividing equation ( ) by equation ( ), 12th - 12th - - - - - Unit Electrostatics . . Superposition principle Coulomb’s law explains the interaction between two point charges.
If there are more than two charges, the force on one charge due to all the other charges needs to be calculated. Coulomb’s law alone does not give the answer. The superposition principle explains the interaction between multiple charges. According to this superposition principle, the total force acting on a given charge is equal to the vector sum of forces exerted on it by all the other charges.
Consider a system of n charges, namely q , q , q …. q n . The force on q exerted by the charge