Question

time varying electric field produces magnetic field is based on the phenomenon of

Answer 1

Maxwell's displacement current

Answer 2

The phenomenon where a time-varying electric field produces a magnetic field is based on Maxwell's displacement current, which is incorporated into the Ampere-Maxwell law.

Explanation:

The original Ampere's Circuital Law stated that a magnetic field is produced by a conduction current. However, James Clerk Maxwell identified an inconsistency in this law when applied to time-varying fields (e.g., charging a capacitor). To resolve this, he proposed the existence of a "displacement current" ($I_d$), which arises due to a changing electric flux. This displacement current acts as a source of magnetic field, similar to a conduction current.

Maxwell modified Ampere's law to include this term, resulting in the Ampere-Maxwell law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 (I_c + I_d)$ where $I_c$ is the conduction current and $I_d = \epsilon_0 \frac{d\Phi_E}{dt}$ is the displacement current. The term $\frac{d\Phi_E}{dt}$ represents the rate of change of electric flux, which is directly related to a time-varying electric field. This modification completed the set of Maxwell's equations and provided the theoretical foundation for the existence and propagation of electromagnetic waves.

Answer:

The phenomenon is based on Maxwell's displacement current (or the Ampere-Maxwell Law).