MCAT content library / Chemistry & physics / Magnetic forces on moving charges
Use velocity, charge sign, and field direction to predict magnetic deflection without confusing a change in direction with a change in kinetic energy.
About 16 minutes, including the charged-particle trajectory example and checks.
Useful foundations
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Magnetic force depends on motion
A charged particle in a magnetic field experiences a magnetic force only when its velocity has a component perpendicular to the field. The magnitude is
F = |q|vB sin θ
where θ is the angle between the particle’s velocity and the magnetic field. A particle moving exactly parallel or antiparallel to the field has no magnetic force from that field. A particle moving perpendicular to the field experiences the maximum magnetic force for the given speed, charge magnitude, and field strength.
Concept: use the right-hand rule for positive charge
For a positive charge, point the fingers of your right hand in the velocity direction and curl toward the magnetic-field direction; the thumb indicates the magnetic-force direction. For a negative charge, reverse that direction.
The force is perpendicular to both the velocity and the magnetic field. That geometry means a uniform magnetic field can continually redirect a moving particle without pushing it faster along its instantaneous direction of motion.
Worked application: predict a particle path
An original beam experiment sends positively charged particles to the right through a region where the magnetic field points into the page. The particles enter perpendicular to the field.
Using the right-hand rule for a positive charge, velocity points right and the field points into the page. The magnetic force initially points upward. As the particle begins curving upward, the force remains perpendicular to its instantaneous velocity, producing circular motion in the uniform-field model.
For a particle moving perpendicular to the field, equating magnetic force with centripetal force gives:
|q|vB = mv²/r
so
r = mv/(|q|B).
| Change | Predicted effect on radius |
|---|---|
| Double mass, same v, q, B | Radius doubles |
| Double speed, same m, q, B | Radius doubles |
| Double |q|, same m, v, B | Radius halves |
| Double B, same m, v, q | Radius halves |
A negative particle with the same mass, speed, and charge magnitude would curve with the same radius but in the opposite direction.
Pattern: magnetic force can bend a path without doing work
Because the magnetic force is perpendicular to velocity, the instantaneous magnetic work on the particle is zero in this ideal model. The field changes the direction of velocity but not its speed. Kinetic energy therefore remains constant while the trajectory bends.
This is a useful distinction from an electric field. An electric force can have a component parallel or antiparallel to velocity and can therefore change the particle’s speed and kinetic energy.
Rule: electric and magnetic forces do different things
A stationary charge can feel an electric force but no magnetic force from a static magnetic field. A moving charge can feel both. In crossed electric and magnetic fields, the two forces can even oppose one another. A passage may exploit this to create a velocity selector: particles with one particular speed pass undeflected when electric and magnetic force magnitudes balance.
If the electric field is perpendicular to the magnetic field and to the particle velocity, the undeflected condition is qE = qvB, giving v = E/B. Charge magnitude cancels, but the directions still matter.
ACTIVE PRACTICE · MAGNETIC FORCE
Change Radius Without Changing Speed
The original particle enters rightward perpendicular to a uniform magnetic field into the page. For a positive charge, the initial magnetic force is upward. Use r = mv/(|q|B) and |F| = |q|vB. All controls are factors relative to an unspecified reference particle; output radii and forces are dimensionless ratios.
Orbit radius: × reference. Magnetic-force magnitude: × reference.
Initial deflection: upward. Speed and kinetic energy remain constant during ideal magnetic-only motion.
Factors are relative to a baseline at the same perpendicular entry geometry. The magnetic field alone produces zero instantaneous work; no electric forces or radiative losses are modeled.
Check your reasoning
Choose an answer before opening its feedback.
Check 1
A positive charge moves to the right while the magnetic field points into the page. What is the initial magnetic-force direction?
A. Upward
Correct. Right-hand-rule geometry gives an upward force for a positive charge.
B. Downward
Review this choice. That would be the direction for a negative charge under the same velocity and field.
C. Into the page
Review this choice. The force is perpendicular to the field.
D. To the right
Review this choice. The magnetic force is perpendicular to velocity.
Check 2
A charged particle enters a uniform magnetic field parallel to the field lines. What magnetic force does it experience?
A. Zero
Correct. sin 0° = 0.
B. Maximum upward force
Review this choice. Maximum force requires perpendicular motion.
C. A force proportional to v²
Review this choice. The magnetic-force magnitude is |q|vB sin θ.
D. Infinite force
Review this choice. Parallel motion gives zero magnetic force.
Check 3
A particle moves perpendicular to a magnetic field in a circle. If the magnetic-field strength doubles while all other quantities remain unchanged, what happens to the radius?
A. It halves.
Correct. r = mv/(|q|B).
B. It doubles.
Review this choice. Radius is inversely proportional to B.
C. It remains unchanged.
Review this choice. Field strength is in the denominator of the radius relation.
D. The particle must stop.
Review this choice. A magnetic field can change direction without reducing speed in the ideal model.
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