Question:
Which one of the following laws is modified by Maxwell to obtain four electromagnetic equations known as Maxwell's equations?
Which one of the following laws is modified by Maxwell to obtain four electromagnetic equations known as Maxwell's equations?
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The four Maxwell's equations are:
1. Gauss's Law of Electrostatics
2. Gauss's Law of Magnetism
3. Faraday's Law of Induction
4. Ampere-Maxwell Law (the only one modified by Maxwell).
1. Gauss's Law of Electrostatics
2. Gauss's Law of Magnetism
3. Faraday's Law of Induction
4. Ampere-Maxwell Law (the only one modified by Maxwell).
Updated On: Jul 22, 2026
- Gauss's law of electricity
- Gauss's law of magnetism
- Faraday's law
- Ampere's circuit law
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
The question asks which of the classical laws of electromagnetism was modified by James Clerk Maxwell to formulate his set of four fundamental equations.
Step 2: Key Concept and Approach:
Maxwell identified an inconsistency in Ampere's Circuital Law when applied to circuits with time-varying electric fields, such as a charging capacitor.
To resolve this, he introduced the concept of displacement current, modifying Ampere's law into the Ampere-Maxwell Law.
Step 3: Detailed Explanation:
• Inconsistency in Ampere's Law:
Ampere's Circuital Law is written as:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 I_c \] During the charging of a capacitor, a magnetic field exists between the plates, but no conduction current ($I_c$) flows there, causing a mathematical contradiction.
• Maxwell's Correction:
Maxwell proposed that a changing electric field between the plates induces a magnetic field, acting as a virtual current called the displacement current ($I_d$):
\[ I_d = \varepsilon_0 \frac{d\Phi_E}{dt} \] He modified Ampere's law to include this term:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 \left( I_c + \varepsilon_0 \frac{d\Phi_E}{dt} \right) \] This modified equation is called the Ampere-Maxwell Law.
Step 4: Final Answer:
The law modified by Maxwell is Ampere's circuit law, which corresponds to Option (D).
The question asks which of the classical laws of electromagnetism was modified by James Clerk Maxwell to formulate his set of four fundamental equations.
Step 2: Key Concept and Approach:
Maxwell identified an inconsistency in Ampere's Circuital Law when applied to circuits with time-varying electric fields, such as a charging capacitor.
To resolve this, he introduced the concept of displacement current, modifying Ampere's law into the Ampere-Maxwell Law.
Step 3: Detailed Explanation:
• Inconsistency in Ampere's Law:
Ampere's Circuital Law is written as:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 I_c \] During the charging of a capacitor, a magnetic field exists between the plates, but no conduction current ($I_c$) flows there, causing a mathematical contradiction.
• Maxwell's Correction:
Maxwell proposed that a changing electric field between the plates induces a magnetic field, acting as a virtual current called the displacement current ($I_d$):
\[ I_d = \varepsilon_0 \frac{d\Phi_E}{dt} \] He modified Ampere's law to include this term:
\[ \oint \vec{B} \cdot d\vec{l} = \mu_0 \left( I_c + \varepsilon_0 \frac{d\Phi_E}{dt} \right) \] This modified equation is called the Ampere-Maxwell Law.
Step 4: Final Answer:
The law modified by Maxwell is Ampere's circuit law, which corresponds to Option (D).
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