Electric Field

An electric field is the region surrounding a charge particle which can influence other charged particles. Since electrostatic force acts on a pair of charged particles, a single charged particle does not actually exert any force. However, if we were to put another charged particle in proximity to this one, a force would be applied. That proximity is the electric field.

Definition §

Assume we have a point charge, $A$ and a point charge $B$ to act as reference. The electric field of $A$, ${\vec{E}}_A$ is the force exerted on $B$ by $A$ divided by the charge on $B$, $q_B$

Formula §

$${\vec{E}}_A=\frac{{\vec{F}}_{AonB}}{q_B}=k_e\times \frac{q_A}{r^2}\times \hat{u}=\frac{1}{4\pi {ϵ}_0}\times \frac{q_A}{r^2}\times \hat{u}$$

• ${\vec{E}}_A$ = Electric field originating from $A$ ($N/C$ or $V/m$)
• ${\vec{F}}_{AonB}$ = Electrostatic force on $B$ by $A$ $(N)$
• $q_B$ = Charge of $B$ (the test charge)
  

In depth: §

If you know what an Electrical Potential is, then the electrical field can also be defined through the electrical potential:

$$\vec{E}=-\nabla V$$

• $\nabla$ = Gradient Vector
• $V$ = Electrical Potential (in $V$)

Visualising §

We can use field lines to visualise the electric field around a point. Because the electric field is a vector field, we can observe the direction from the field lines to identify the force. However, there are some important rules:

• Field lines point outwards from positive charges and point inwards to negative charges
• They cannot intersect or touch
• The density of the field lines is used to identify the field strength, not the length of the field lines. I.e. areas where there is a lot of field lines bunched up indicate a stronger electric field. Also, charge density is proportional to field line density.
• Areas where the electric field is 0 is marked with a dot or a gap
• Conventionally, the number of field lines for a given charge, $q$, is $\frac{q}{{ϵ}_0}$
• Cannot form a loop

Field lines stem from positive?

Field lines are just a visual guide, and physics convention has been to use positive test charges and most likely due to that we have field lines extending from positive charges. I.e. a test charge (which is positive) will be repelled from a positive charge

Superposition §

Because electric fields are essentially vector fields, vector superposition also applies to them, just like it does electrostatic force.

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