Magnetic Force on a Charge
Force on a moving charge in a magnetic field.
Formula
Variables
How it works
A charged particle moving through a magnetic field experiences a sideways force because the magnetic field acts on moving charges, not on charges at rest. The force depends on how fast the charge moves, how strong the field is, and the angle between the velocity and the field: it is greatest when the motion is perpendicular to the field and zero when the motion is parallel to it. This is why the force does no work on the particle directly; it changes the direction of motion rather than the speed.
When to use it
Use this formula when a single charged particle or ion is moving through a magnetic field, such as in mass spectrometers, particle beams, and the motion of electrons in magnetic devices. It is also used when analyzing circular motion caused by magnetic forces, like in cyclotrons or plasma physics.
Worked example, step by step
A proton with charge q = 1.60 × 10^-19 C moves at v = 3.0 × 10^6 m/s through a magnetic field of B = 0.40 T at an angle of θ = 90° to the field. Step 1: Write the formula: F = qvB sinθ Step 2: Substitute the values: F = (1.60 × 10^-19)(3.0 × 10^6)(0.40) sin(90°) Step 3: Since sin(90°) = 1, simplify: F = (1.60 × 10^-19)(3.0 × 10^6)(0.40) Step 4: Multiply the numbers: 1.60 × 3.0 × 0.40 = 1.92 Step 5: Combine the powers of ten: 10^-19 × 10^6 = 10^-13 Step 6: Final result: F = 1.92 × 10^-13 N
Common mistakes to avoid
- using the formula for a stationary charge, when magnetic force requires motion
- forgetting the sine factor and assuming the force is always qvB
- mixing up the angle with the complementary angle between the field and the perpendicular direction
Did You Know?
A magnetic force always acts sideways to a charge's motion, so it changes direction but never speed.
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