## What is Coulomb's laws?

The force of interaction of two stationary point charges in vacuum is directly proportional to the product of these charges and inversely proportional to the square of their separation.K=9.0 x 10

^{9}N•m

^{2}/C

^{2}

Îµ0= 8.85×10

^{−12}F⋅m

^{−1 }(farads per metre).

#### Important points Regarding Coulomb's Law:-

Principle of superposition:-

How to solve a problem using Coulomb's law?

Coloumb's law in vector form:-

Example:;

How to solve a problem using Coulomb's law?

Coloumb's law in vector form:-

Example:;

This is law is valid for point charges. Colombian force or electrostatics force is a conservative force. This force follow Newton's third law. It is two particle interaction that means force of interaction between two charge particle does not depends on presence or absence of third charge. Magnitude of this force follow Inverse Square Law.

Where, K is a constant which depends on the System of units. its value in SI unit is

The constant of often written in the form

Where,Îµ0 is called the permittivity constant which is numerically equal to

The coulomb force acts along the straight line joining the points of location of the charges. This force is central and spherically symmetric.

**The vector form of Coulomb's law is**

r= distance between both given charges.

**Felect = 9.23 x 10-7 N**

◆【1】Charges are assumed to be at rest. when charges are in motion they also produce and experience magnetic forces. ◆【2】Charges are assumed to be on point Particles.

◆【3】Coulomb's law cannot be applied directly to a finite charge distribution. There is a difference when the charge is distributed uniformly over a spherical surface, the force on a point charge outside the surface may be computed from coulombs law by trenting the charge on the sphere as if it were concentrated at the centre. For charged body of finite size, there is no well defined value of the separation 'r' and integration is required.

◆【3】 the force is conservative in nature that means work done by electrostatic force in moving a point charge along a closed loop of any shape is zero.

The Coulomb's law obeys the principle of superposition, which means that the force between two particles is not affected by a presence of other charges . This principle is used to find the net force exerted on a given particle by other charged particle.

◆【1】Decided whether the force due to a given charge it attractive or repulsive and Express it by drawing vectors.

◆【2】Find the magnitude of the force using coulomb's law ignoring the signs of the charges.

◆【3】Resolve the forces along the given co-ordinate Axes and Express them in vector form using i^,j^,k^ vector notation useless otherwise specified.

◆【4】Use the principle of superposition to find the net force on a charge.

●Four point positive charges q are located at the corners of a square as shown in the figure. Find the net force acting on the charge at D.

Solution;

#### Coulomb's law Derivation:

This law was given by Coulomb scientist. According to this law-
The force acting between charge is directly proportional to the product of both charges and inversely proportional to the square of distance between them.

Let q1 and q2 be two point charges separated and a distance of 'r' if electrostatics force 'f' is applied between them, then according to coulomb's law,

from equation (1) and (2)

Where, 'K' is Constant called electrostatics constant.

【Îµ0 = permittivity not】

F ∝ q1q2 _(1) and

F ∝ 1/r2_____(2).

Fv∝ q1q2/de

F = K.q1q2/r2

K = 1/4Ï€Îµ0

●The Unit of "K".

●Dimension of K is [ ML3T-4A-2 ].

Dimension of Îµ0 is [ M-1L-3T4A2 ].

●Numerical value of ' K' is

K = 9×10

^{9}Nm2/C2 = 1/4Ï€Îµ_{0}
K = 1/4Ï€Îµ

_{0}Îµr
When Îµr is given.

●Unit of 'Îµ

_{0}' is
●Numerical value of 'Îµ0' is:-

Îµ

_{0}=8.854×10^{−}^{12}F⋅m^{−}^{1}(farads per metre).
Îµ

_{0}= permittivity of free space.
Îµm/E = permittivity of given medium.

Îµr = Relative permittivity.

The value of Relative permittivity with respect to air is 1.

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