Question

drive the equation of coulomb's law?​

Answer 1

Answer:

Coulomb's law explains the electrostatic force at a given distance squared. It's stated as: Force = (k) x (e1) x (e2) / r^2. The real source of Coulomb's law is the creation of an electron 'charge' in accordance with E = M x C^2.

Answer 2

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When solving a problem in electricity and magnetism I always first look at Maxwell’s Equations.

∮E⃗ ⋅dA→=qϵ0 (Gauss’s Law)

∮B⃗ ⋅dA→=0 (Gauss’s Law for Magnetism)

∮E⃗ ⋅dl→=−dΦBdt (Faraday’s Law)

∮B⃗ ⋅dl→=μ0(I+ϵ0dΦEdt) (Ampere-Maxwell Law)

Coulomb’s Law relates force to charge and Gauss’s Law relates electric field to charge so that looks like the equation to use. Enclose the single charge q in a sphere of radius r . Because of symmetry, the electric field will be the same everywhere on the sphere’s surface. The left hand side of Gauss’s Law then reads

∮E⃗ ⋅dA→=E∮dA=EA=E4πr2

becuase the area of a sphere is 4πr2 .

We’re left with E4πr2=

$\frac{q}{e0}$

or solving for the E-field

E=$\frac{1}{4\pi \: e0} \: \frac{q}{ {r}^{2} }$

Noting that the force on a particle with charge Q is F=QE so our final result is

F=$\frac{1}{4\pi \: e0} \: \frac{qQ}{ {r}^{2} }$

We have proved Coulomb’s Law!

Thanx❤✌