EM-03 · Electrostatics field

The Electric Field

A charge creates a vector field, the electric field, in the space around it. See for yourself that the arrow is the force a unit charge would feel, fading as the inverse square of distance.

Change the distance and the sign

Look at the charge from near and from far. As the distance changes, watch the force arrow on the test charge. As the sign flips, watch the direction reverse.

The buttons flip the sign of the source charge.

Distance r to the test charger = 1.60

Drag to orbit. Slider for distance, buttons for the charge sign.

The field E at this point

Outward (away from the charge)

E = kQ/r² r̂ · radial, falls off as 1/r²

F = qE · the force on a test charge q

Relative field strength · 47%

Near · strong field ·

The electric field — a charge's map of force

Put down a single charge, and at every surrounding point an arrow appears saying "a unit positive charge placed here would feel this force." The collection of these arrows is the electric field E. Whether or not a test charge is actually present, the field is already spread around the charge. So we define it as E = F/q.

A point charge's field — radial, 1/r²

The field of a point charge Q spreads equally in all directions. Its magnitude falls off as the inverse square of distance: E = kQ/r², directed along the radial unit vector r̂. For a positive charge it points outward, for a negative one inward. The constant k is 1/(4πε₀).

ObserveE = k Qr² r̂

A point charge's field is proportional to Q and inverse to r².

Force comes from the field — F = qE

Place any charge q in an electric field and the force on it is F = qE, the field arrow times the amount of charge. The key point is that the field E does not depend on the test charge q. Double q and the E at that spot is unchanged; only the force doubles. The field is a property of the source charge that made it.

ChooseF = ?

Force is charge times field.

Direction and adding up

The field points out of positive charges and into negative ones. With several charges, you add the arrow from each one as vectors to get the field at a point (superposition). When charge is spread along a line, surface, or volume, that sum becomes an integral — the subject of the next unit.

Fill in|E| ∝ ?

Twice the distance, a quarter of the field.

On your ownE = ? r̂

The constant k is 1/(4πε₀).

Back to the first screen

As you slid the test charge closer, the force arrow grew sharply: halve the distance and the field quadruples, because it goes as 1/r². Press the sign button and every arrow flips at once — direction follows the sign of the charge. And however you changed the test charge, the background field arrows stayed put, because the electric field belongs not to the charge placed in it but to the charge that made it.

The electric field E is a vector field a charge creates in the space around it. The arrow at a point equals the force a unit positive charge placed there would feel (E = F/q). For a point charge Q it is E = kQ/r² r̂, radial and inversely proportional to the square of the distance. The force on a charge q is F = qE.

What comes next

The electric field is the protagonist of electrostatics, and from here it branches two ways. When charge is spread over a line, surface, or volume, you integrate dE to get the whole field (EM-04). And counting how much of this field pierces a closed surface leads to flux and divergence (EM-05) and the Gauss law (EM-06).