Electronic – At t=0 the voltage across the Inductor will immediately jump to battery voltage. Why


While reading transients i come to read……

"the voltage across the inductor will immediately jump to battery voltage (acting as though it were an open-circuit) and decay down to zero over time (eventually acting as though it were a short-circuit)."

Why the inductor voltage will immediately jump to battery voltage. They say that thats because of the time changing magnetic field across the inductor that will induce equal and opposite voltage in the inductor according to Lenz-Law. But then at t= 0 they claim that the current is zero in the inductor. So when the current is zero in the Inductor then how a magnetic field can be built to induce opposite voltage across the inductor.

So whats happening at t=0 ? zero current and equal and opposite volage ? Since there is zero current then what makes the inductor voltage equal to battery voltage ? If there is current at t=0 then why its never mentioned anywhere in theory or in equation ?

Best Answer

  1. Switch closes. Electric field starts to propagate in the wire, much faster than electrons.
  2. Maxwell equation number 4 says:

    The magnetic field induced around a closed loop is proportional to the electric current plus displacement current (rate of change of electric field) it encloses.

which is defined by the fourth formula here:

enter image description here

Check the differential form. At the very moment of closing the switch, the current is 0, therefore the current density (J) is 0. However, as the electric field arrives to the inductor, a sudden change in electric field induces a very high magnitude rotational magnetic field.

  1. Due to Lenz' law, another electric field will be induced to resist this sudden magnetic field, in the opposite direction. Thus, a counter electric potential is formed, without any currents involved. You can search the phenomena "Displacement field" to see how this magic occurs.