Question

State and prove coulomb's law. Explain coulomb's law in vector form.

Answer 1

Answer:

The Coulomb's law states that the force between two point charges are inversely proportional to the square of the distance between the charges and is directly proportional to the product of magnitude of the two charges.

F = k(q1q2)/r²

The constant k is usually put as 1/4πε0.

Hence, the law can be written as : F = 1/4πε0×(q1q2)/r².

Here, ε0 = 8.854A×10^(-12) C²N^-1m^-2

We know Force is a vector. So, let us prove the law in vector form.

Let us assume the two point charges q1 and q2 all are kept in xy plane whose position vectors are r1 and r2.

Now, The magnitude is |r21| and the direction is denoted by r-hat 21 = (r21)/(|r21|). (It's the vector leading from 1 to 2)

Now, Coulomb's law : F = (1/4πε0)×((q1q2)/r²21)×(r-hat 21)

Similarly for r-hat 12, F = (1/4πε0)×((q1q2)/r²12)×(r-hat 12)