AcademyMagnetic Fields and Forces
Academy
Magnetic Fields
Level 1 - Physics topic page in Magnetic Fields and Forces.
Principle
A magnetic field is defined by the force it exerts on moving charge.
Notation
\(\vec F_B\)
magnetic force on a particle
\(\mathrm{N}\)
\(q\)
particle charge
\(\mathrm{C}\)
\(\vec v\)
particle velocity
\(\mathrm{m\,s^{-1}}\)
\(\vec B\)
magnetic field
\(\mathrm{T}\)
\(\theta\)
angle between velocity and field
\(\mathrm{rad}\)
Method
Magnetic force depends on the component of velocity perpendicular to the field.
Vector law
\[\vec F_B=q\vec v\times\vec B\]
Magnitude
\[F_B=|q|vB\sin\theta\]
Perpendicular speed
\[v_{\perp}=v\sin\theta\]
Force magnitude
\[F_B=|q|v_{\perp}B\]
Use the right-hand rule for \(\vec v\times\vec B\). Reverse the direction for a negative charge.
Rules
Magnetic force
\[\vec F_B=q\vec v\times\vec B\]
Force magnitude
\[F_B=|q|vB\sin\theta\]
Tesla
\[1\,\mathrm{T}=1\,\mathrm{N\,C^{-1}\,m^{-1}\,s}\]
No work
\[\vec F_B\cdot\vec v=0\]
Examples
Question
A proton moves perpendicular to a
\[0.20\,\mathrm{T}\]
field at \[3.0\times10^5\,\mathrm{m\,s^{-1}}\]
Find \(F_B\).Answer
\[F_B=qvB=(1.60\times10^{-19})(3.0\times10^5)(0.20)=9.6\times10^{-15}\,\mathrm{N}\]
Checks
- Only the perpendicular component of velocity matters.
- Positive and negative charges curve in opposite directions.
- The force is perpendicular to both \(\vec v\) and \(\vec B\).