Question

Two identical charges separated by a distance r are moving in the same direction with velocity v. Prove
that the ratio of magnetic and electric forces acting between them is (v/c)^2 where c is speed of light in
vacuum.​

Answer 1

pls tell for which class is this

Answer 2

Thus the ration between the magnetic and electric forces is FB / FE =  v^2 / c^2

Explanation:

The electric force between the two protons is given as

 F(E) = 1/4πε0 x q^2/r^2

Now, the magnetic force is given as FB = qvB

To find B:

The magnetic field is given from Biot-Savarts law as

FB =  μo q^2 v^2 / 4πr^2 / q^2 / 4πε0r^2 =  μo ε0 v^2

Speed of light is given as:

C =  1/ √ 1 /  μoε0

c^2 = 1 / μoε0

μoε0 = 1 / c^2

The ratio is:

FB / FE = μoε0v^2 = v^2 / c^2

Thus the ration between the magnetic and electric forces is FB / FE =  v^2 / c^2