Force

Prof. Dr. Thorsten Jungmann (last updated 2025-09-03)

Force (German: Kraft) is the cause of a change in the state of motion (acceleration) of a body. In electrical engineering, force acts, for example, on electric charges and current-carrying conductors in electric and magnetic fields respectively.

Vector quantity in a homogeneous field → scalar quantity

This is a vector quantity. In this script, however, it is conventionally treated as a scalar quantity in the context of the homogeneous field (for a detailed justification).

1 Quantity symbol and unit

The quantity symbol of force is the letter $F$.
Its unit (SI) is the newton (N):

$$[F]=\mathrm{N}=\mathrm{kg}\cdot \frac{\mathrm{m}}{{\mathrm{s}}^2}$$

2 Practical and worked examples

Basic relationship (Newton’s second law): $F=m\cdot a$

2.1 Weight-force (from the mass):

$F_{\mathrm{g}}=m\cdot g,g\approx 9.81\frac{\mathrm{m}}{{\mathrm{s}}^2}$
Example: $m=2.0\mathrm{kg}\Rightarrow F_{\mathrm{g}}\approx 19.6\mathrm{N}$

2.2 Electric force on an electric charge in a homogeneous field:

$F=q\cdot E$
Example: $q=1\mathrm{nC},E=5kV/m\Rightarrow F=5\mu \mathrm{N}$

2.3 Magnetic force on a current-carrying conductor (perpendicular to $\vec{B}$):

$F=B\cdot I\cdot l$
Example: $B=0.5\mathrm{T},I=2\mathrm{A},l=0.10\mathrm{m}\Rightarrow F=0.10\mathrm{N}$

3 Typical orders of magnitude

• Weight of a 1 kg body: $\approx 9.81\mathrm{N}$
• Pressing a key with a finger: $\approx 1\mathrm{N}$
• Pulling force of small electromagnets: $\approx 1\dots 20\mathrm{N}$

4 Example phrasings

• ‘The weight-force is 9.87 newtons.’
• ‘In the field, the force $F=5\mu \mathrm{N}$ (micronewtons) acts on the electric charge.’
• ‘The conductor experiences a magnetic force of 0.1 newtons.’

5 Related quantities

• Mechanical work: $W=F\cdot s$
• Pressure: $p=\frac{F}{A}$
• Relates to electrical engineering quantities: electric field strength $E$, magnetic flux density $B$, electric charge $q$, energy $W$

6 Related components

• Relay and contactor (force in the magnetic field)
• Inductor (force effect in the magnetic field, e.g. electromagnet)