Relation Cross-Scans

Force Charge Field Two-Factor Scan

F = qE

Force from a field is a product. Charge and field each get a three-row scan before the final force is read.

Example

Force from a field is a product. Charge and field each get their own three-row scan before the final force is read. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start from a local field

At point P, the checked field arrow has size 5 newtons per coulomb. The positive test charge is 2 coulombs.

E=5 N/Cqtest=2 CE=5\ \text{N/C}\qquad q_{\text{test}}=2\ \text{C}
Force from fieldThe field arrow and force arrow are both checked.+3 Csource+2 Ctest5 N/C10 N

Multiply copies of force per charge

A charge of 2 coulombs carries 2 copies of the per-coulomb force.

F=qtestEF=q_{\text{test}}E

Compute the force

Multiplying 2 coulombs by 5 newtons per coulomb gives 10 newtons.

F=2 C⋅5 N/C=10 NF=2\ \text{C}\cdot 5\ \text{N/C}=10\ \text{N}
Force from fieldThe rendered force is the middle scan row.+3 Csource+2 Ctest5 N/C10 N

Scan charge at fixed field

Hold field fixed at 5 newtons per coulomb. Three rows show force growing directly with test charge.

qtestEF1 C5 N/C5 N2 C5 N/C10 N4 C5 N/C20 N\begin{array}{c|c|c}q_{\text{test}}&E&F\\1\ \text{C}&5\ \text{N/C}&5\ \text{N}\\2\ \text{C}&5\ \text{N/C}&10\ \text{N}\\4\ \text{C}&5\ \text{N/C}&20\ \text{N}\\\end{array}

Scan field at fixed charge

Hold charge fixed at 2 coulombs. A larger field makes a larger force on the same charge.

qtestEF2 C3 N/C6 N2 C5 N/C10 N2 C7 N/C14 N\begin{array}{c|c|c}q_{\text{test}}&E&F\\2\ \text{C}&3\ \text{N/C}&6\ \text{N}\\2\ \text{C}&5\ \text{N/C}&10\ \text{N}\\2\ \text{C}&7\ \text{N/C}&14\ \text{N}\\\end{array}
Force from fieldThe same point P carries both product scans.+3 Csource+2 Ctest5 N/C10 N
electrostatics Read force as copies of a local field, one copy per coulomb of test charge.