The time varying electric field is | Electrical MCQ | Examoogle

Back to Practice Questions

ElectricalElectromagnetics Field Theory

Prev Next

The time varying electric field is

$E = -\nabla V$

$E = -\nabla V - \frac{\partial A}{\partial t}$

$E = -\nabla V - B$

$E = -\nabla V - D$

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalElectromagnetics Field Theory

Option B

$E = -\nabla V - \frac{\partial A}{\partial t}$

Quick Summary:

In time-varying electromagnetic fields, the electric field is not purely conservative; it is defined by both the gradient of a scalar potential and the time derivative of a magnetic vector potential. This is a direct consequence of Faraday's Law combined with the vector identity for a curl-free magnetic field.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$E = -\nabla V - \frac{\partial A}{\partial t}$ — The general definition of electric field in dynamic fields

$\nabla \times E = -\frac{\partial B}{\partial t}$ — Faraday's Law of Induction

⚙️ Working Principle

According to Faraday's law, $\nabla \times E = -\frac{\partial B}{\partial t}$ . Since the magnetic flux density $B$ can be expressed as the curl of a vector potential $A$ (where $B = \nabla \times A$ ), substituting this into Faraday's law gives $\nabla \times (E + \frac{\partial A}{\partial t}) = 0$ . Since the curl of the sum is zero, the term $(E + \frac{\partial A}{\partial t})$ can be represented as the gradient of a scalar potential $V$ , leading to the relation $E = -\nabla V - \frac{\partial A}{\partial t}$ .

📌 Key Points

▸
In static fields, $E = -\nabla V$ (conservative field).
▸
In time-varying fields, the changing magnetic field induces an electric field component proportional to $\frac{\partial A}{\partial t}$ .
▸
The scalar potential $V$ and vector potential $A$ fully characterize the electromagnetic field.

✅ Advantages

▸
Unifies electrostatics and magnetodynamics.
▸
Allows for potential-based analysis of radiation problems.

❌ Disadvantages / Limitations

▸
Requires knowledge of vector calculus.
▸
Potential functions are not uniquely defined without gauge conditions.

🛠️ Applications / Uses

▸
Waveguide propagation analysis.
▸
Antenna theory and radiation modeling.
▸
Electromagnetic compatibility (EMC) testing.

📄 Additional Information

▸
The term $\frac{\partial A}{\partial t}$ represents the non-conservative (induced) electric field.
▸
Option B is the standard convention in EM theory, where $A$ is the magnetic vector potential and $\frac{\partial A}{\partial t}$ is its partial time derivative.

📊 Diagram / Illustration

✅

B is correct — The electric field in a time-varying system is the sum of the gradient of the scalar potential $V$ and the time derivative of the magnetic vector potential $A$ .

Core Concepts Used

Click any tag to open in AI Tutor

Faraday's Law Magnetic Vector Potential Scalar Electric Potential

💡 EXAM TIP

Always verify if the field is static or time-varying. In static cases, the second term vanishes, simplifying to the gradient of the scalar potential.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)