Electric Charges and Fields - Electric Field and Field Lines

Electric Field: It is the environment around a charge where another charge experiences an electrostatic force. The Electric Field Intensity $\vec{E}$ is defined as the force experienced per unit positive test charge $q_0$, given by $\vec{E} = \frac{\vec{F}}{q_0}$.

Electric Field due to a Point Charge: For a source charge $Q$, the magnitude of the field at a distance $r$ is inversely proportional to the square of the distance, following the Inverse Square Law.

Principle of Superposition: The net electric field at a point due to a system of point charges is the vector sum of the electric fields produced by each charge individually: $\vec{E}_{net} = \vec{E}_1 + \vec{E}_2 + ... + \vec{E}_n$.

Electric Field Lines: These are continuous curves used to represent the electric field visually. The tangent to a field line at any point gives the direction of $\vec{E}$ at that point. They never intersect because at the point of intersection, there would be two directions of the electric field, which is impossible.

Properties of Field Lines: They start from positive charges and end at negative charges. The density of field lines in a region indicates the relative strength of the electric field.

Electric Dipole: A pair of equal and opposite charges $q$ and $-q$ separated by a distance $2a$. The electric dipole moment $\vec{p}$ is a vector directed from $-q$ to $+q$.

Electric Field of a Dipole: The field at an axial point (distance $r$) is directed along the dipole moment, while at an equatorial point, it is opposite to the dipole moment. For a short dipole ($r \gg a$), the axial field is twice the equatorial field.