5aMagnetic Fields and Forces
Explore how magnetic fields exert forces on moving charges and current-carrying wires using F = qvB sinθ and the right-hand rule.
Magnetic forces on moving charges underpin electric motors, particle accelerators, MRI machines, and the compass — understanding them connects fundamental physics to modern technology.
Lesson Overview
Magnetic fields exert forces on moving charges and current-carrying wires. In this lesson you will learn how to calculate the magnetic force using F = qvB sinθ and F = BIL sinθ, apply the right-hand rule to determine force direction, and understand how magnetic field lines represent field direction and strength — including Earth's own magnetic field.
Key Concepts
Magnetic Field (B)
A vector field measured in tesla (T) that exerts force on moving charges
Force on a Charge
F = qvB sinθ; maximum when velocity ⊥ field, zero when parallel
Right-Hand Rule
Point fingers in v direction, curl toward B — thumb points in direction of F (positive charge)
Force on a Wire
F = BIL sinθ; depends on current I, length L, and angle θ between wire and B
Magnetic Field Lines
Exit north pole, enter south pole outside magnet; inside magnet S → N
Earth's Magnetic Field
Geographic north ≈ magnetic south pole; field ≈ 25–65 μT at surface
A proton (q = 1.6 × 10⁻¹⁹ C) moves at 3.0 × 10⁶ m/s perpendicular to a magnetic field of 0.50 T. Calculate the magnetic force on the proton.
An electron moves parallel to a magnetic field of 2.0 T at 5.0 × 10⁵ m/s. What is the magnetic force on it?
A wire carries a current of 4.0 A and has a length of 0.30 m in a 0.80 T field perpendicular to the wire. Find the force on the wire.
Using the right-hand rule, determine the direction of force on a positive charge moving east in a magnetic field pointing north.
A wire of length 0.50 m carrying 2.0 A makes a 30° angle with a 1.2 T magnetic field. Calculate the force on the wire.
An alpha particle (q = 3.2 × 10⁻¹⁹ C) moves at 2.0 × 10⁶ m/s at 90° to a 0.40 T field. Find the magnetic force.
Hint: Use F = qvB sinθ with θ = 90°, so sinθ = 1.
A 0.20 m wire carries 5.0 A perpendicular to a magnetic field. The force on the wire is 0.40 N. Find B.
Hint: Rearrange F = BIL sinθ for B. With θ = 90°, B = F / (IL).
A negative charge moves west in a field pointing upward. In which direction is the magnetic force?
Hint: Apply the right-hand rule for a positive charge first, then reverse the direction for a negative charge.
Why do magnetic field lines never cross each other?
Hint: Think about what crossing field lines would imply about the direction of the field at that point.
Earth's magnetic field near the surface is about 50 μT. A wire of length 1.0 m carries 10 A perpendicular to this field. Calculate the force.
Hint: Convert μT to T first (50 μT = 5.0 × 10⁻⁵ T), then use F = BIL.
Key Vocabulary
Magnetic Field (B)
A region of space where a magnetic force acts on moving charges or magnetic materials; measured in tesla (T).
Example: The magnetic field between two bar magnets is strongest near the poles.
Tesla (T)
The SI unit of magnetic field strength; 1 T = 1 N/(A·m).
Example: An MRI machine uses a magnetic field of 1–3 T, far stronger than Earth's field.
Right-Hand Rule
A mnemonic for finding the direction of magnetic force: point fingers in the direction of velocity, curl toward B; thumb points in the direction of force on a positive charge.
Example: Using the right-hand rule, a proton moving east in a northward field experiences an upward force.
Magnetic Force
The force exerted on a moving charge or current-carrying conductor by a magnetic field; F = qvB sinθ or F = BIL sinθ.
Example: The magnetic force causes a current-carrying wire to deflect when placed between magnet poles.
Interactive Practice — 5 Questions
What is the SI unit of magnetic field strength?
A charge moves parallel to a magnetic field. The magnetic force on it is:
Which rule determines the direction of force on a positive charge moving through a magnetic field?
A 0.10 m wire carries 3.0 A perpendicular to a 2.0 T field. What is the force on the wire?
Outside a bar magnet, magnetic field lines run from:
Independent Practice
A proton moves at 4.0 × 10⁶ m/s at 60° to a 0.30 T field. Calculate the magnetic force on it (q = 1.6 × 10⁻¹⁹ C).
A wire of length 0.40 m carries 6.0 A at 45° to a 1.5 T magnetic field. Find the force on the wire.
Explain why a stationary charge experiences no magnetic force even in a strong magnetic field.
Describe the pattern of magnetic field lines around a bar magnet, both inside and outside the magnet.
★ A charged particle moves in a circle inside a uniform magnetic field. Derive an expression for the radius of the circular path in terms of m, v, q, and B.
ChallengeCommon Mistakes
Using F = qvB without including sinθ, giving the wrong answer when v and B are not perpendicular.
Always use F = qvB sinθ; only when θ = 90° does sinθ = 1 and F = qvB.
Thinking magnetic field lines go from south to north outside the magnet.
Field lines exit the north pole and enter the south pole outside; inside the magnet they go from S to N.
Applying the right-hand rule result directly to negative charges.
The right-hand rule gives force direction for positive charges; for negative charges, reverse the direction.
Math Tips
For F = qvB sinθ: identify θ as the angle between the velocity vector and the magnetic field vector — not the angle of the path.
Units check: [T] = [N/(A·m)], so [B][I][L] = [N/(A·m)][A][m] = [N]. ✓