Two point electric charges q1 and q2 at rest, separated by a distance r exert a force on each other whose magnitude is given by
If between the two charges there is free space then
Where ε0 is the absolute electric permittivity of the free space and ε0 = 8.85 x 10-12 C2 / N-m2
Illustration 1. A polythene piece rubbed with wool is found to have negative charge of 3.2 x 10-7 C.
(a) Estimate the number of electrons transferred from wool to polythene.
(b) Is there a transfer of mass from wool to polythene? If yes, how much?
Solution: (a) Let n be the number of electrons getting transferred.
⇒ n x e = 3.2 x 10-7
⇒ 1.6 x 10-19 n = 3.2 x 10-7
⇒ n = 2 x 1012 ⇒ 2 x 1012 electrons will get transferred.
(b) Mass transferred will be product of number of electrons and the mass of electron.
If m = mass getting transferred.
⇒ m = n x (9.1 x 10-31) kg
m = 2 x 1012 x 9.1 x 10-31
m = 18.2 x 10-31 kg
Illustration 2. Calculate force between two charges of 2 C each separated by 2 m in vacuum.
Solution: F = kQ1Q2/R2 = 9 x 109 x 2 x 2 ⇒ F = 9 x 109 N
Illustration 3. Two particles A and B having charges 8 x 10-6 C and –2 x10-6 C respectively are held fixed with a separation of 20 cm. Where should a third charged particle be placed so that it does not experience a net electric force?
Solution: As the net electric force on C should be equal to zero, the force due to A and B must be opposite in direction. Hence, the particle should be placed on the line AB. As A and B have charges of opposite signs, C cannot be between A and B. Also A has larger magnitude of charge than B. Hence, C should be placed closer to B than A. The situation is shown in figure. Suppose BC=x and the charge on C is Q
Illustration 4. A charge of -2 μC is placed at the perpendicular bisector of the line joining two point charges of 10 μC as shown in figure. What is the net force acting on the -2 μC charge ?
Components of forces parallel to AB will cancel out.
F = F1 cos θ + F2 cos θ
Questions For You:
(i) A negatively charged particle is placed exactly midway between two fixed particles having equal positive charge. What will happen to the charge ?
(a) if it is displaced at right angle to the line joining the positive charges?
(b) if it is displaced along the line joining the positive charges?
(ii) Is the Coulomb force between two given charges affected in anyway, if other charges are brought in the neighbourhood ?
Coulombs law in Vector Relations
PRINCIPLE OF SUPERPOSITION
This principle tells us that if charge Q is placed in the vicinity of several charges q1, q2 ….. qn, then the force on Q can be found out by calculating separately the forces F1 ,F2 …Fn , exerted by q1, q2, ….. qn respectively on Q and then adding these forces vectorially. Their resultant F is the total force on Q due to all of charges.
Illustration 5. It is required to hold equal charges q each in equilibrium at the corners of a square of
side a. What charge when placed at the centre of the square will do this?
Let the charge be Q
As ABCD is a square of side a, r=a/√2
Net force on the charge at B is
For charge q to be in equilibrium at B, the net force on it must be zero. Taking x-component