Which of the following statements is/are correct?

Statements:

1) Ampere's Law describes the relationship between electric current and the magnetic field it produces.

2) Maxwell's equations are a set of four fundamental equations governing electric and magnetic fields in the absence of charges and currents.

Question

Which of the following statements is/are correct?

Statements:

1) Ampere's Law describes the relationship between electric current and the magnetic field it produces.

2) Maxwell's equations are a set of four fundamental equations governing electric and magnetic fields in the absence of charges and currents.

Accepted Answer

**Solution:**

1. **Statement 1:** Ampere's Law indeed explains the connection between an electric current and the magnetic field it generates. It states that the magnetic field around a current-carrying conductor is proportional to the current enclosed. Mathematically, it is expressed as:

$$\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I$$

where $\mathbf{B}$ is the magnetic field, $d\mathbf{l}$ is an infinitesimal element of the path, $\mu_0$ is the permeability of free space, and $I$ is the current enclosed by the path.

2. **Statement 2:** Maxwell's equations are a set of four fundamental equations that describe how electric and magnetic fields behave. However, these equations account for the presence of charges and currents, not just their absence. They include Gauss's law, Gauss's law for magnetism, Faraday's law of induction, and Ampere's law with Maxwell's correction. Therefore, the claim that Maxwell's equations govern fields only in the absence of charges and currents is incorrect.

**Answer:** Only Statement 1 is correct.

Answer

Answer

Answer