To calculate the magnetic force on a charge moving in a magnetic field, you will use the equation that properly incorporates the values of the charge, the velocity, the magnetic field strength, and the angle between the velocity and the magnetic field. The correct equation for magnetic force [tex]\( F \)[/tex] is given by:
[tex]\[ F = |q| v B \sin(\theta) \][/tex]
Where:
- [tex]\( |q| \)[/tex] is the magnitude of the charge,
- [tex]\( v \)[/tex] is the velocity of the charge,
- [tex]\( B \)[/tex] is the strength of the magnetic field,
- [tex]\( \theta \)[/tex] is the angle between the velocity vector and the magnetic field vector.
Let's analyze the provided options:
1. [tex]\( F = |q| v B \cos(\theta) \)[/tex]: This is incorrect because it uses [tex]\(\cos(\theta)\)[/tex] instead of [tex]\(\sin(\theta)\)[/tex].
2. [tex]\( F = |q| v B \sin(\theta) \)[/tex]: This is correct because it correctly includes [tex]\(\sin(\theta)\)[/tex] term.
3. [tex]\( F = |q| B \cos(\theta) \)[/tex]: This is incorrect because it omits the velocity [tex]\( v \)[/tex] and incorrectly employs [tex]\(\cos(\theta)\)[/tex].
4. [tex]\( F = |q| B \sin(\theta) \)[/tex]: This is incorrect because it omits the velocity [tex]\( v \)[/tex].
Hence, the correct equation to calculate the magnetic force on a charge moving in a magnetic field is:
[tex]\[ F = |q| v B \sin(\theta) \][/tex]
