answrsearchWhat would you like to ask?12thPhysicsMoving Charges and MagnetismLorentz ForceTwo protons move parallel t...PHYSICSTwo protons move parallel to each other, keeping distance r between them, both moving with same velocity v . Then the ratio of the electric and magnetic force of interaction between them is:(c - Velocity of light) HARDShareStudy laterANSWERThere are two forces electric force and magnetic force experienced by proton.The electric force between the two protons is given as F E = 4πε 0 1 r 2 q 2 Now, the magnetic force isF B =qvBB is the magnetic field.From Biot- savarts LAWB= 4πμ 0 r 2 IdL dL is the length ELEMENT of the conductor but, the expression will be for charge where is no current.So,we KNOW that,I= TQ IdL=q dtdL IdL=qvNow, the magnetic field is B= 4πμ 0 r 2 qv The magnetic force isF B =qvBF B =qv 4πμ 0 r 2 qv F B = 4πμ 0 r 2 q 2 v 2 Now, the ratio of the electric force and the magnetic force isF B F E = 4πμ 0 × r 2 q 2 v 2 4πε 0 1 × r 2 q 2 F B F E = μ 0 ε 0 v 2 1 ......(I)We know that, the speed of lightc= μ 0 ε 0 1 c 2 = μ 0 ε 0 1 Now, PUT the value of μ 0 ε 0 1 in equation (I)F B F E = v 2 c 2 Hence, the ratio of electric force and magnetic force will be F B F E = v 2 c 2 .