State coulomb's law. give its formula and explain each term.
Answers
Mathematical expression of columb's force is given by
F= kq1q2/r²
where K is constant = 9x10^9Nm²/C²
r= distance between the centres of the two charges.
Answer:
according to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges.
Table of Content
Coulomb’s Law Formula
Coulomb’s Law in Vector Form
What is One Coulomb of Charge
Key Points
Limitations
Relative Permittivity
Applications
Problems
Coulomb’s Law Formula
Coulombs law 1
In Short: F ∝ q1q2/d2
where,
ε is absolute permittivity,
K or εr is the relative permittivity or specific inductive capacity
ε0 is the permittivity of free space.
K or εr is also called a dielectric constant of the medium in which the two charges are placed.
History of Coulomb’s Law
A French physicist Charles Augustin de Coulomb in 1785 coined a tangible relationship in mathematical form between two bodies that have been electrically charged. He published an equation for the force causing the bodies to attract or repel each other which is known as Coulomb’s law or Coulomb’s inverse-square law.
Coulomb’s Law in Vector Form
Coulombs law 2
Here F12 is the force exerted by q1 on q2 and F21 is the force exerted by q2 on q1.
Coulomb’s law holds for stationary charges only which are point sized. This law obeys Newton’s third law
Force on a charged particle due to a number of point charges is the resultant of forces due to individual point charges i.e.
What is 1 Coulomb of Charge?
A coulomb is that charge which repels an equal charge of the same sign with a force of 9×109 N, when the charges are one meter apart in a vacuum. Coulomb force is the conservative mutual and internal force.
The value of εo is 8.86 × 10-12 C2/Nm2 (or) 8.86 × 10-12 Fm–1
Note: Coulomb force is true only for static charges.
Coulomb’s Law – Conditions for Stability
If q is slightly displaced towards A, FA increases in magnitude while FB decreases in magnitude. Now the net force on q is toward A so it will not return to its original position. So for axial displacement, the equilibrium is unstable.
If q is displaced perpendicular to AB, the force FA and FB bring the charge to its original position. So for perpendicular displacement, the equilibrium is stable.
Key Points on Coulomb’s Law
1. If the force between two charges in two different media is the same for different separations,
= constant .
2. Kr2 = constant or K1r12 = K2r22
3. If the force between two charges separated by a distance ‘r0’ in a vacuum is the same as the force between the same charges separated by a distance ‘r’ in a medium, then from Coulomb’s Law; Kr2 = r02
4. Two identical conductors having charges q1 and q2 are put to contact and then separated after which each will have a charge equal to
. If the charges are q1 and –q2, then each will have a charge equal to
5. Two spherical conductors having charges q1 and q2 and radii r1 and r2 are put to contact and then separated the charges of the conductors after contact is;
q1 = [r1/(r1 + r2)] (q1 + q2) and q2 = [r2/(r1 + r2)] (q1 + q2)
6. If the force of attraction or repulsion between two identical conductors having charges q1 and q2 when separated by a distance d is F. Also if they are put to contact and then separated by the same distance the new force between them is
7. If charges are q1 and -q2 then, F = F(q1 + q2)2 / 4q1q2
8. Between two-electrons separated by a certain distance: Electrical force/Gravitational force = 1042
9. Between two protons separated by a certain distance: Electrical force/Gravitational force = 1036
10. Between a proton and an electron separated by a certain distance: Electrical force/Gravitational force = 1039
11. The relationship between the velocity of light, the permeability of free space and permittivity of free space is given by the expression c = 1 / √ (μoεo )
12. If Coulomb’s law is applied to two identical balls of mass m are hung by silk thread of length ‘l’ from the same hook and carry similar charges q then;
The distance between balls =
The tension in the thread =
\(\begin{array}{l}\sqrt{f^2 + (mg)^2}\end{array} \)
If the total system is kept in space then the angle between threads is 180° and tension in a thread is given by
T =
A charge Q is divided into q and (Q – q). Then electrostatic force between them is maximum when
Limitations of Coulomb’s Law
The law is applicable only for the point charges at rest.
Coulomb’s Law can be only applied in those cases where the inverse square law is obeyed.
It is difficult to implement Coulomb’s law where charges are in arbitrary shape because in such cases we cannot determine the distance’ between the charges.