Charge Balance and Separation

Separated Slabs Create Restoring Field

Displaced electron charge sees a restoring force by sign convention. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Separation creates an electric field

A displacement of 2 meters with field gradient 3 newtons per coulomb per meter gives field 6 newtons per coulomb.

3 N/(C*m)⋅2 m=6 N/C3\ \text{N/(C*m)}\cdot 2\ \text{m}=6\ \text{N/C}
Separated electron slabThe field vector points away from the displacement source.electronEFx=2 mgradient=3 N/(C*m)E=6 N/Cq=-1 CF=-6 NK=12 1/s^2density=3massRatio=6omega2=6 1/s^2

A negative charge feels the restoring force

The electron slab charge is -1 coulomb, so the force is -6 newtons and points back.

−1 C⋅6 N/C=−6 N-1\ \text{C}\cdot 6\ \text{N/C}=-6\ \text{N}
Restoring force conventionThe force arrow is checked opposite the field arrow.electronEFx=2 mgradient=3 N/(C*m)E=6 N/Cq=-1 CF=-6 NK=12 1/s^2density=3massRatio=6omega2=6 1/s^2