Maxwell's Equations Questions

The famous scientist and mathematician ‘Maxwell’ was the first to calculate the speed of propagation of electromagnetic waves, almost the same as the speed of light. From the observations, he concluded that electromagnetic waves and visible light are the same. The set of partial differential equations is the base of classical thermodynamics, classical optics and electrical circuits. We can use Maxwell’s equation to explain how the electric current and charges produce the magnetic and electric fields. There are four main Maxwell’s equations.

• Maxwell’s first equation (Gauss’s law for electricity) –
\(\begin{array}{l}\nabla.D = \varrho _{v}\end{array} \)
• Maxwell’s second equation (Gauss’s law for magnetism) –
\(\begin{array}{l}\nabla .B = 0 \end{array} \)
• Maxwell’s third equation (Faraday’s law) –
\(\begin{array}{l}\nabla \times E = -\frac{\partial B}{\partial t}\end{array} \)
• Maxwell’s fourth equation (Ampere – Maxwell’s law) –
\(\begin{array}{l}\nabla \times H = -\frac{\partial D}{\partial t}+J\end{array} \)

Read More – Maxwell’s Equations

Important Questions with Answers

1. What is electromagnetic induction?

The current produced because of voltage production is the electromotive force due to a changing magnetic field; this is called electromagnetic induction.

2. Maxwell’s fourth equation is based on ________.

1. Ohm’s law
2. Ampere’s circuital law
3. Coulomb’s law
4. Faraday’s law

Answer- b. Ampere’s circuital law

Explanation: Maxwell’s fourth equation is based on Ampere’s circuital law. To understand Maxwell’s fourth equation, Ampere’s circuital law is required.

3. State Ampere’s circuital law.

The closed line integral of a magnetic field vector is always equivalent to the entire amount of scalar electric field enclosed within the path of any shape, which means the current flowing along the wire is equal to the magnetic field vector.

4. Maxwell’s first equation is based on _________.

1. Gauss’s law for magnetism
2. Gauss’s law for electrostatic
3. Faraday’s law
4. Ampere’s circuital law

Answer – b. Gauss’s law for electrostatic

Explanation: Maxwell’s first equation is based on Gauss’s electrostatics law. According to Gauss law, the density of an electric flux of a closed surface integral is always equivalent to the charge enclosed over the surface.

5. What are the applications of Maxwell’s equation?

The applications of Maxwell’s equation are as follows:

• Maxwell’s equation can be used to calculate the static electric field in a vacuum.
• It can be used to calculate the magnetic field in a vacuum.
• Maxwell’s equation provides a mathematical model for optical, electric, radio technologies, power generation, lenses, wireless communication, radar etc.

6. What is the Maxwell equation?

The Maxwell equations are the four essential equations of electromagnetism, including Faraday’s law of electromagnetic induction, Gauss’s law of electricity, Ampere’s law of current carrying conductor and Gauss’s law of magnetism.

7. Is it true that Maxwell’s equations are always correct?

When quantum mechanical processes are present, Maxwellian electrodynamics fails, just as Newtonian mechanics must be substituted in that regime by quantum mechanics. These equations do not “fail” because there is always an analogous version in quantum mechanics; it is only the mechanics that vary.

8. Are all four Maxwell’s equations independent?

They are not independent; Maxwell’s equations are a set of coupled partial differential equations.

9. Why did Maxwell modify Ampere’s law?

Maxwell modified Ampere’s law to include the effect of time changing electric fields. Magnetic fields can be created by using time changing electric flux. The Ampere’s law was,

In Ampere’s law, Maxwell observed displacement current (I_d) and the conduction current I together possess the property of continuity along a closed path. Where the displacement current is,

Maxwell added displacement current (I_d ) to the right hand side of Ampere’s law,

This is known as Ampere-Maxwell law.

Maxwell expanded Ampere’s law by presenting the displacement current into the current electric component to fulfil the continuity equation of electric charge.

10. What do Maxwell’s equations explain?

Maxwell’s equations describe how electric charges and currents generate magnetic and electric fields. It explains how an electric field can produce a magnetic field and vice versa.

11. What is displacement current in Maxwell’s equation?

Maxwell’s equations include a term called displacement current. The definition of displacement current is based on the rate of change of the electric displacement field (D).

12. What is the relationship between Ohm’s law and Maxwell’s equation?

Ohm’s law is already one of the original Maxwell’s equation’s eight sets. It is produced by the equation F, which describes the relationship between an electric current and the electromotive force.

Practice Questions

1. State and explain Maxwell’s equations.
2. Define scalar magnetic flux and scalar electric flux. What is the difference between scalar magnetic flux and scalar electric flux?
3. What is the use of Maxwell’s equations in thermodynamics?
4. What is Maxwell’s equation for free space?
5. What is Maxwell’s equation for the static field?

To learn more about Maxwell’s equation, watch the video below.

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