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Electromagnetism
How Electric and Magnetic Fields Create Forces
Electromagnetism explains how charged particles feel forces from electric and magnetic fields. Electric fields push or pull charges along the field direction depending on the sign of the charge. Magnetic fields deflect moving charges sideways, changing their direction without directly changing their speed. These ideas are central to motors, generators, particle accelerators, speakers, power grids, and many modern sensors.
A charge in an electric field feels a force F = qE, so a positive charge accelerates with the field and a negative charge accelerates against it. A moving charge in a magnetic field feels a force F = qvB sin(theta), directed perpendicular to both its velocity and the magnetic field. Together, the electric and magnetic forces combine into the Lorentz force, F = qE + qv x B. This single rule predicts how charges curve, speed up, spiral, or separate in real electromagnetic systems.
Key Facts
- Electric force on a charge: F = qE.
- Magnetic force on a moving charge: F = qvB sin(theta).
- Lorentz force: F = qE + qv x B.
- A magnetic force is zero if the charge is at rest or moves parallel to the magnetic field.
- For circular motion in a uniform magnetic field: r = mv/(|q|B).
- Electric fields can change a particle's speed, while magnetic fields change the direction of its motion when perpendicular to velocity.
Vocabulary
- Electric field
- A region around charges where another charge experiences an electric force.
- Magnetic field
- A region around magnets or moving charges where moving charges and magnetic materials can experience forces.
- Lorentz force
- The total electromagnetic force on a charge due to electric and magnetic fields.
- Right-hand rule
- A method for finding the direction of magnetic force on a positive moving charge using the directions of velocity and magnetic field.
- Field line
- A drawn line that shows the direction a positive test charge or magnetic north pole would tend to move.
Common Mistakes to Avoid
- Treating electric and magnetic forces as the same kind of push is wrong because electric forces act on charges whether they move or not, while magnetic forces require motion.
- Forgetting the sin(theta) factor in F = qvB sin(theta) is wrong because only the part of velocity perpendicular to the magnetic field creates magnetic force.
- Using the right-hand rule for negative charges without reversing the answer is wrong because the magnetic force direction flips when q is negative.
- Assuming a magnetic field always changes a particle's speed is wrong because magnetic force is perpendicular to velocity and usually changes direction, not kinetic energy.
Practice Questions
- 1 A proton with charge 1.60 x 10^-19 C is in a uniform electric field of 2.5 x 10^4 N/C. What is the magnitude of the electric force on the proton?
- 2 An electron moves at 3.0 x 10^6 m/s perpendicular to a 0.20 T magnetic field. Using |q| = 1.60 x 10^-19 C, what is the magnitude of the magnetic force?
- 3 A positive charge moves to the right through a magnetic field pointing into the page. In which direction is the magnetic force, and how would the direction change if the charge were negative?