If relativity tells that from a moving charge's frame (observing current carrying wire) protons contract in length and its charge density increases making the charge experience a electrostatic force. In lab frame (observing current carrying wire and a stationary charged particle) the electrons are moving in wire, will they contract in length and make the charge feel electrostatic force? But this is not observed as only moving charges near a current carrying wire feel the force and not a stationary one. Help me imagine. Try intuitive way to explain. I am 12th grade student.
I think, from the viewpoint of the lab observer, the diameter of each electron is Lorentz contracted in the direction of motion, whereas the distance between every two successive electrons remains unchanged. This causes the charge density of the moving electrons to be unchanged, and thus there is no net electric field. However, the observer who is located in the electrons' rest frame detects that not only the diameter of each proton but also the distance between every two protons is Lorentz contracted, which causes the charge density of the moving protons to increase.