Question

What is Maxwell's first equation?

Answer 1

Maxwell's first equation is known as Gauss's Law, which describes the relationship between electric charge and electric field. In its integral form, it states that the electric flux through a closed surface is proportional to the charge enclosed within that surface:

\[
\Phi_E = \oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\epsilon_0}
\]

Here, \(\Phi_E\) is the electric flux, \(\mathbf{E}\) is the electric field, \(d\mathbf{A}\) is a differential area vector on the closed surface, \(Q_{\text{enc}}\) is the total charge enclosed by the surface, and \(\epsilon_0\) is the permittivity of free space.

In differential form, Gauss's Law can be expressed as:

\[
\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}
\]

where \(\rho\) is the charge density. This equation highlights how electric fields are generated by electric charges.

Answer 2

Maxwell's First Equation is one of the fundamental equations of electromagnetism, and it describes how electric fields are generated by electric charges. It's known as Gauss's Law for Electricity. Mathematically, it is expressed as:

\[ \nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0} \]

where:
- \(\nabla \cdot \mathbf{E}\) is the divergence of the electric field \(\mathbf{E}\),
- \(\rho\) is the electric charge density,
- \(\epsilon_0\) is the permittivity of free space.

In integral form, Gauss's Law is:

\[ \oint_{\partial V} \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\epsilon_0} \]

where:
- \(\oint_{\partial V} \mathbf{E} \cdot d\mathbf{A}\) is the electric flux through a closed surface,
- \(Q_{\text{enc}}\) is the total electric charge enclosed within the surface.

This equation essentially states that the electric flux through a closed surface is proportional to the total charge enclosed by that surface.