Electromagnetism · 01 / 06

Charge & Electric Fields

A source charge changes the space around it. The electric field tells what force a positive test charge would experience at each location.

The learner question

What exists between two charged objects before the second object even arrives?

The electric field belongs to the source configuration and space around it. A test charge samples that field. Changing the test charge changes the force, but it does not redefine the pre-existing field in this model.

Two linked relationships
E=kQr2E = k\frac{|Q|}{r^2}
F=qE\mathbf F = q\mathbf E

The field comes from the source charge QQ. The force also depends on the test charge qq.

Field sampler

Change the source, distance, and test charge independently.

point is to the right of Q
+
source Q
+
E
F
test q
distance
2.00 m
field magnitude
4.50e+3 N/C
force on q
4.49e-3 N
Source charge Q2.0 μC
Distance r2.0 m
Test charge q1.0 μC
field idea
Direction is defined with a positive test charge

Electric field points in the direction a positive test charge would accelerate: away from positive sources and toward negative sources.

field idea
A negative test charge reverses force, not field

The source field stays the same. Since F = qE, a negative q makes the force point opposite the electric field.

field idea
Distance matters quadratically

For a point charge, doubling the distance reduces the field magnitude to one quarter. The inverse-square structure spreads influence over growing spherical area.

Field is local

At each point in space, E tells the force-per-positive-charge that a small test charge would experience there.

Superposition comes next

With several source charges, add their electric-field vectors. Each source contributes independently to the total field.

Force depends on the traveler

The same electric field can push positive and negative charges in opposite directions and with different magnitudes.

Transfer check

You double the distance from a point charge but change nothing else. What happens to the electric-field magnitude?

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