Question

drive expression of coulombs the law in electrostatics​

Answer 1

Answer:

Coulomb's law, or Coulomb's inverse-square law, is an experimental law[1] of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called electrostatic force[2] or Coulomb force.[3] The quantity of electrostatic force between stationary charges is always described by Coulomb's law.[4] The law was first published in 1785 by French physicist Charles-Augustin de Coulomb, and was essential to the development of the theory of electromagnetism, maybe even its starting point,[5] because it was now possible to discuss quantity of electric charge in a meaningful way.[6]

In its scalar form, the law is:

{\displaystyle F=k_{\text{e}}{\frac {q_{1}q_{2}}{r^{2}}},} {\displaystyle F=k_{\text{e}}{\frac {q_{1}q_{2}}{r^{2}}},}

where ke is Coulomb's constant (ke ≈ 8.99×109 N⋅m2⋅C−2),[7] q1 and q2 are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if like-signed (i.e., F is positive).

Being an inverse-square law, the law is analogous to Isaac Newton's inverse-square law of universal gravitation, but gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive.[8] Coulomb's law can be used to derive Gauss's law, and vice versa. In the case of a single stationary point charge, the two laws are equivalent, expressing the same physical law in different ways.[9] The law has been tested extensively, and observations have upheld the law on a scale from 10−16 m to 108 m.[10]

Explanation:

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Answer 2

Answer:

Coulomb’s Law In Vector Form

Let the position vectors of charges q1 and q2 be r1 and r2 respectively Fig.We denote force on q1 due to q2 by F12 and force on q2 due to q1by F21. The two point charges q1 and q2 have been numbered 1 and 2 for convenience and the vector leading from 1 to 2 is denoted by r21:

r21 = r2 – r1. In the same way, the vector leading from 2 to 1 is denoted by r12: r12 = r1 – r2 = – r21 .The magnitude of the vectors r21 andr12 is denoted by r21 and r12, respectively (r12 = r21). The direction of a vector is specified by a unit vector along the vector. To denote the direction from 1 to 2 (or from 2 to 1), we define the unit vectors:

 Coulomb’s force law between two point charges q1 and q2 located at r1 and r2 is then expressed as

If q­1 and q2 are of the same sign (either both positive and both negative), F21 is along ˆr 21, which denotes repulsion, as it should be for like charges. If q1 and q2 are of opposite signs, F21 is along – ˆr 21(= ˆr 12), which denotes attraction, as expected for unlike charges.

Explanation: