📘 Magnetic Force
A magnetic field doesn’t just sit there—it exerts a force. However, magnetism is “picky.” A magnetic field will only exert a force on a charge if that charge is moving. If the particle stops, the force vanishes.
Audio Explanation
Prefer to listen? Here's why velocity and direction are the keys to unlocking magnetic force.
Force on a Moving Charge
When a particle with charge $q$ moves with a velocity $v$ through a magnetic field $B$, it experiences a force. The magnitude of this force depends on the angle between the velocity and the field.
\[F_B = qvB\sin\theta\]- $F_B$: Magnetic Force (Newtons, N)
- $q$: Charge (Coulombs, C)
- $v$: Velocity (m/s)
- $B$: Magnetic Field Strength (Tesla, T)
- $\theta$: The angle between the velocity vector and the magnetic field vector.
The “Zero Force” Rule
If a charge moves parallel or anti-parallel to the magnetic field lines ($\theta = 0^\circ$ or $180^\circ$), the force is zero. Magnetic force is at its maximum when the charge moves perpendicular to the field.
The Right-Hand Rule (RHR)
Magnetic force is always perpendicular to both the velocity and the magnetic field. To find the direction of the force for a positive charge, use your right hand:
- Fingers: Point them in the direction of the velocity ($v$).
- Curl: Curl them toward the magnetic field ($B$).
- Thumb: Your thumb points in the direction of the Magnetic Force ($F_B$).
Note for Electrons: If the charge is negative (like an electron), the force points in the opposite direction of your thumb!
Visual Representation: Circular Motion
Because the magnetic force is always perpendicular to the velocity, it acts as a centripetal force. This causes charged particles to fly in circles when they enter a uniform magnetic field.
Interactive Particle Chamber
Fire a proton into a magnetic field. Change the speed of the particle or the strength of the field to see how the radius of its circular path changes.
Cloud Chamber Simulator
Force on a Current-Carrying Wire
Since a current is just a bunch of moving charges, a wire with electricity flowing through it also feels a magnetic force.
\[F = ILB\sin\theta\]- $I$: Current (Amperes, A)
- $L$: Length of the wire in the field (meters, m)
This is the principle behind the electric motor. By placing a coil of wire in a magnetic field and running a current through it, the magnetic force creates torque, making the motor spin.
Interactive Match: Force Directions
Use the Right-Hand Rule to determine the direction of the force in these scenarios.
Why Should I Care?
- Mass Spectrometers: Scientists identify chemical elements by shooting them through magnetic fields; heavier atoms curve less than lighter ones.
- Aurora Borealis: Charged particles from the sun get “trapped” by Earth’s magnetic force and spiraled toward the poles, where they hit the atmosphere and glow.
- Speakers: Your headphones use a small electromagnet that is pushed and pulled by a permanent magnet to vibrate a cone and create sound.
💡 Quick Concept Check:
An electron is moving due North through a magnetic field that points straight UP (out of the ground). Which way is the magnetic force pushing the electron?