hey ❣...need a hand.....give the derivation of coulombs law
Answers
Coulomb’s law establishes the force that a “charged particle”, say q1, experiences because of another charged particle, say q2, around it. The force is proportional to the product of charges and inversely proportional to the square of the distance between them. The formula can then be written as -
F = k∙q₁∙q₂/r²
Here q1 and q2 are point charges. (for extended objects carrying a charge, like a rod, triangle etc., there are different mathematical techniques to find the force) and r is the distance between them. The magnitude of the force on q1 or q2 will be the same because of each other. Simply put the force on q1 due to q2 is F and the force on q2 due to q1 is also F.
Here k is the electrostatic constant or the Coulomb constant. Now since force is a vector quantity, we must write this equation in vector form. That brings us to the direction of the force.
The direction of the force depends on the nature of the charge or the sign of the charge on the particle. So if the charge is the same, they will repel each other and the force vectors are directed away from the particle. But, if the particles are carrying opposite charge, the force vectors will be towards each particle. So, if the particles have opposite charge and if we let go of the particles, they will rush towards each other.
Very often the direction of this force is expressed by using the i,j,k vector notation or as a radial vector by multiplying it with a unit radial vector r.
There is also a striking similarity of this law with Newton’s law of gravitation. Both laws have inverse distance square dependence and product of mass in one case and charge in the other. However, gravitational force is always attractive in nature while electrostatic force can be attractive or repulsive. This is obvious since mass is of one type while charges are of two types (+/-)
Coming back to coulombs constant k, it is often written as
k = 1/ 4πϵ0 and is equal to 8.99 X 10^9 N m (sq)/ C (sq).
Here ϵ0 is called the permittivity constant and is equal to 8.85 X 10 -12 C(sq)/ N.m(sq).
A few things to keep in mind-
1. Like all forces, the electrostatic force also follows the principle of superposition or simply put if a particle is experiencing several forces on it due to various charged particles around it, then the net force is given by the vector sum of all forces. So if you know all the forces acting on a particle, then it becomes more of a vector problem.
2. Then there is the Shell theory which is quite the same as what we have in Gravitation. So a charged particle outside a shell, on which the charge is uniformly distributed (that is on the sphere), will experience a force as if the entire charge on the surface of the shell is concentrated as a particle at its center
3. Also, a charged particle inside a shell with a uniform charge on the surface of the shell has no net force acting on it due to the shell
For more information, you can also watch the below video.
^r21=-^r12
F12=-F21
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