# Force without magnetic or electric field

In a long primary solenoid,if we introduce a secondary one on its outer surface,due to mutual inductance-an emf is generated in the secondary one according to Lenz's law if there is a time varying current in the primary coil.

But,

• 1.we know that for an infinite solenoid,there is no magnetic field outside it-hence there is no magnetic field in the secondary coil placed over it.All field is inside the primary coil.

• 2.There is no electric field as the primary coil is electrically neutral overall-irrespective of current flowing through it.

• 3.The electrons in the secondary coil experiences a force which causes the current.

Considering all these together,we can conclude that the electron in secondary coil-which is in a region of no electric or magnetic field still experiences a force.How is it possible?

According to Faraday's Induction Law, the integral form of the Maxwell-Faraday equation $$\oint_{C} {\bf E} \cdot d{\bf l} = -\frac{d}{dt} \int_S {\bf B} \cdot d {\bf S}$$ (valid for stationary surface/boundary), you don't need a magnetic field at the location of the outer coil for an electric field to be induced there according to the time derivative of the magnetic flux. Each winding of the outer coil, the integration path on the LHS of eq. (1), encloses an area, the core of the inner coil, where there is a magnetic flux that changes with time. No magnetic field needs to be at the boundary of the enclosed area $S$ of the integral on the RHS of eq. (1). Thus, for an electric field induced in the outer coil, there needs not be any magnetic field produced by the inner coil at the location of the outer coil, as is the case in the described situation of a perfect, infinite inner coil.
• @user157588 - There is definitely an electric field $\bf E$ that moves the electrons in the outer coil! This is the electric field that appears in the contour integral on the LHS of the Maxwell equation (1). The surprising might only be that this electric field is produced by the changing flux of a magnetic field that is zero at the location of the induced electrical field. Jan 31 '18 at 3:40