UY1: Electric Field Lines

An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric field vector at that point.

To find the field caused by a charge distribution, imagine the distribution to be made up of many point charges, $q_{1}$, $q_{2}$, $q_{3}$, …

At any given point $P_{1}$, each point charge produces its own electric field $\vec{E}_{1}$, $\vec{E}_{2}$, $\vec{E}_{3}$, …

A test charge $q_{0}$ placed at P will experience a total force of:

$$\vec{F}_{0} = q_{0}\vec{E}_{1} + q_{0}\vec{E}_{2} + q_{0}\vec{E}_{3} + …$$

The total electric field at point P will then be:

$$\vec{E} = \frac{\vec{F}_{0}}{q_{0}} = \vec{E}_{1} + \vec{E}_{2} + \vec{E}_{3} + …$$

This is the principle of superposition of electric fields.

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