Question

Maxwells equations are derived from the laws of (A) electricity (B) magnetism (C) both electricity and magnetism (D) mechanics

Short answer

(C) both electricity and magnetism

Step-by-step solution

An overview of Maxwell's Equations

Maxwell's equations consist of four equations that govern the behavior of electric and magnetic fields. They are: 1. Gauss's Law for Electricity: \[\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enclosed}}}{\epsilon_0}\] 2. Gauss's Law for Magnetism: \[\oint \mathbf{B} \cdot d\mathbf{A} = 0\] 3. Faraday's Law of Induction: \[\oint \mathbf{E} \cdot d\mathbf{l} = - \frac{d\Phi_B}{dt}\] 4. Ampere's Law with Maxwell's Addition: \[\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 (I_{\text{enclosed}} + \epsilon_0 \frac{d\Phi_E}{dt})\] Now let's briefly discuss the origin of each equation.

Gauss's Law for Electricity

Gauss's Law for Electricity is derived from the electric field created by a charged particle. The electric field produced by charged particles is an aspect of the laws of electricity.

Gauss's Law for Magnetism

Gauss's Law for Magnetism states that there are no isolated magnetic poles, i.e., no magnetic monopoles. The magnetic field is always produced in closed loops. This law is related to the laws of magnetism.

Faraday's Law of Induction

Faraday's Law of Induction describes how a changing magnetic field induces an electric field, i.e., a voltage that can cause a current to flow. This law is related to electromagnetism, a combination of both electricity and magnetism.

Ampere's Law with Maxwell's Addition

Ampere's Law with Maxwell's Addition describes the relationship between electric currents and the magnetic fields they generate. Maxwell's addition includes the effect of a changing electric field that causes a magnetic field. This law is also related to electromagnetism.

Conclusion

As we see that Maxwell's equations involve aspects of both electricity and magnetism, the correct answer is: (C) both electricity and magnetism