Electronics Engineering (ELEX) Board Practice Exam

Which equation represents the time-varying electric field?

1. E = ▽V + A

2. E = ▽V - A

3. E = V / A

4. E = V * A

The correct answer is: E = ▽V - A

The equation that correctly represents the time-varying electric field is derived from the relationship between electric potential (voltage) and electric field, along with the influence of any time-varying magnetic fields represented by the vector potential (A). In electromagnetic theory, particularly in the context of Maxwell's equations, the electric field (E) is related to the gradient of the electric potential (V) and can also involve the vector potential (A) when magnetic fields are varying with time. The term ▽V represents the spatial variation of voltage, which contributes to the electric field, while the vector potential accounts for any changes implying the presence of a magnetic field. Choosing the appropriate sign is crucial due to the properties of how electric and magnetic fields interplay. In this context, the correct formulation incorporates how the vector potential feeds into the electric field, taking into account the influence of time-variant magnetic fields, which is correctly captured in the selected equation. Thus, this formulation aligns with the principles of electromagnetism that govern how electric fields are generated and vary over time.