Electric Field At A Point

The electric field of a point charge is, like any electric field, a vector field that represents the effect that the point charge has on other charges around it. The event is felt as a force, and when charged particles are not in motility, this force is known as the electrostatic force. The electrostatic force is, much similar gravity, a forcefulness that acts at a distance. Therefore, we rationalize this activity at a altitude by proverb that charges create fields around them that have furnishings on other charges.

Given a signal charge, or a particle of infinitesimal size that contains a certain accuse, electric field lines emanate radially in all directions. If the accuse is positive, field lines signal radially abroad from it; if the charge is negative, field lines signal radially towards information technology .

Electrical field of positive point charge

The electric field of a positively charged particle points radially abroad from the accuse.

Electrical field of negative point charge

The electric field of a negatively charged particle points radially toward the particle.

The reason for these directions can be seen in the derivation of the electrical field of a point accuse. Permit's first take a look at the definition of the electric field of a point particle:

$\displaystyle{\vec{East} = \frac{1}{four\pi\epsilon_o}\frac{q}{r^2}\hat{r} = yard\frac{q}{r^2}\hat{r}}$

The higher up equation is defined in radial coordinates, which can be seen in . The constant thou is a result of simply combining the constants together, and q is the accuse of the particle creating the electrical field. This charge is either positive or negative. If the charge is positive, equally shown higher up, the electric field volition be pointing in a positive radial management from the charge q (away from the accuse).

Every bit a demonstration of this phenomenon, if we now place some other positive charge, Q (chosen the test charge), at some radial distance, R, abroad from the original particle, the test charge will experience a force given by

$\displaystyle{\vec{F} = Q\vec{East} = Q\frac{ane}{4\pi\epsilon_o}\frac{q}{R^2}\chapeau{r}}$

Radial Coordinate Organisation

The electrical field of a point charge is defined in radial coordinates. The positive r management points away from the origin, and the negative r management points toward the origin. The electric field of a betoken charge is symmetric with respect to the θdirection.

The thing to keep in mind is that the force to a higher place is acting on the exam charge Q, in the positive radial direction every bit defined past the original charge q. This means that because the charges are both positive and volition repel one some other, the force on the test accuse points away from the original charge.

If the test charge were negative, the force felt on that accuse would be:

$\vec{F} = Q\vec{E} = -Q\frac{i}{4\pi\epsilon_o}\frac{q}{R^2}\chapeau{r}$

Notice that this points in the negative $\hat{r}$ management, which is toward the original charge. This makes sense considering opposite charges concenter, and the force on the examination accuse volition tend to push it toward the original positive charge creating the field. The higher up mathematical description of the electrical field of a signal charge is known as Coulomb'southward law.