Physics Chapter 1: Electric Charges and Fields

An electric dipole is a pair of equal and opposite charges separated by a small distance. The dipole moment is a vector quantity representing the strength and direction of the dipole.

Electric flux is the measure of the electric field passing through a given surface. It is defined as the dot product of the electric field and the area vector of the surface. Its SI unit is Volt-meter (Vm).

Coulomb's law is valid for point charges only, meaning charges with negligible size in comparison to the distance between them. It also fails to hold true for rapidly moving charges as it doesn't account for relativistic effects.

The electric dipole moment is a vector quantity representing the strength and direction of an electric dipole. It is defined as the product of the magnitude of either charge and the distance between them. Its SI unit is Coulomb-meter (Cm).

Gauss's theorem states that the total electric flux through any closed surface is proportional to the net charge enclosed by the surface. It is mathematically represented as the integral of the dot product of the electric field and the area vector over the closed surface.

Electric flux is the measure of the electric field passing through a given surface. There are two types of flux: Positive flux, when the electric field lines enter the surface, and negative flux, when they leave the surface.

Coulomb's law states that the force of attraction or repulsion between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The unit charge is defined as the charge that exerts a force of 1 Newton on an equal and similar charge placed 1 meter away in vacuum. This law is applicable for static charges at rest, small compared to the distance between them, in a vacuum or a medium of low permittivity.

The intensity of electric field at a point is defined as the force experienced by a unit positive charge placed at that point. Its SI unit is Newton per Coulomb (N/C) or Volt per meter (V/m).

Electric lines of force are imaginary lines representing the direction of the electric field at a point. Four properties of electric lines of force are:

1. The lines start from a positive charge and end on a negative charge.
2. The lines never intersect each other.
3. The electric field is tangent to the line of force at a point.
4. The density of lines of force is proportional to the strength of the electric field.

When a surface is parallel to the electric field, the angle between the electric field and the area vector of the surface is 90 degrees. The dot product of the electric field and the area vector becomes zero, hence the flux through the surface is zero.

The electric field intensity at a point on the axial position of an electric dipole is given by: E = (1/4πε₀) * (2p/r³) where p is the dipole moment, r is the distance from the center of the dipole, and ε₀ is the permittivity of free space.

The electric field intensity at a point on the equatorial position of an electric dipole is given by: E = (1/4πε₀) * (p/r³) where p is the dipole moment, r is the distance from the center of the dipole, and ε₀ is the permittivity of free space.

Gauss's theorem states that the total electric flux through any closed surface is proportional to the net charge enclosed by the surface. This can be proven by considering a closed surface containing a point charge and applying Coulomb's law to find the electric field at each point on the surface. The total flux through the surface is then calculated by integrating the dot product of the electric field and the area vector over the entire surface.

Gauss’s theorem states that the total electric flux through any closed surface is proportional to the net charge enclosed by the surface. This theorem can be used to derive Coulomb’s inverse square law. By applying Gauss’s theorem to a spherical surface enclosing a point charge, we can obtain the electric field at any point on the surface. This electric field is then used to calculate the force between two point charges, which is consistent with Coulomb’s law.

The electric field intensity at a point on the axial position of an electric dipole is given by: E = (1/4πε₀) * (2p/r³) where p is the dipole moment, r is the distance from the center of the dipole, and ε₀ is the permittivity of free space.

The electric field intensity at a point on the equatorial position of an electric dipole is given by: E = (1/4πε₀) * (p/r³) where p is the dipole moment, r is the distance from the center of the dipole, and ε₀ is the permittivity of free space.

Gauss's theorem states that the total electric flux through any closed surface is proportional to the net charge enclosed by the surface. This can be proven by considering a closed surface containing a point charge and applying Coulomb's law to find the electric field at each point on the surface. The total flux through the surface is then calculated by integrating the dot product of the electric field and the area vector over the entire surface.

Gauss’s theorem states that the total electric flux through any closed surface is proportional to the net charge enclosed by the surface. This theorem can be used to derive Coulomb’s inverse square law. By applying Gauss’s theorem to a spherical surface enclosing a point charge, we can obtain the electric field at any point on the surface. This electric field is then used to calculate the force between two point charges, which is consistent with Coulomb’s law.