F_B = qvB sin θ in AP Physics 2

F_B = qvB sin θ is the AP Physics 2 equation for the magnitude of the magnetic force on a moving charged object, where q is the charge, v is its speed, B is the magnetic field strength, and θ is the angle between the velocity and magnetic field vectors (Topic 12.2).

What is F_B = qvB sin θ?

F_B = qvB sin θ tells you how hard a magnetic field pushes on a moving charge. The force grows with three things working together. More charge, more speed, or a stronger field all mean a bigger force. The sin θ factor handles geometry. When the velocity is perpendicular to the field (θ = 90°), sin θ = 1 and the force is at its maximum. When the charge moves parallel or antiparallel to the field (θ = 0° or 180°), sin θ = 0 and the magnetic force vanishes entirely. A charge coasting along a field line feels nothing.

The equation only gives you the magnitude. The direction comes from the right-hand rule, and per the CED (12.2.B.2.ii), the force is always perpendicular to both the velocity and the magnetic field. For a negative charge, flip the direction the right-hand rule gives you. That perpendicular force is the whole personality of magnetism. It can bend a charge's path, but it can never speed it up or slow it down, because a force perpendicular to velocity does zero work. Also notice the v in the equation. A stationary charge feels no magnetic force at all. Magnetism is strictly a moving-charge interaction.

Why F_B = qvB sin θ matters in AP® Physics 2

This equation lives in Topic 12.2 (Magnetism and Moving Charges) in Unit 12 and directly supports learning objective 12.2.B, describing the force exerted on moving charged objects by a magnetic field. Essential knowledge 12.2.B.2.i lists it as the relevant equation, spelling out that the force is proportional to charge, speed, and field strength, and depends on the angle between v and B. It pairs with 12.2.A, which covers the field a moving charge produces, so Topic 12.2 is really two sides of one coin. Moving charges make magnetic fields, and magnetic fields push on moving charges. Almost every magnetism problem you'll see, from mass spectrometers to velocity selectors, starts by writing this equation down. For the full topic treatment, head to the 12.2 study guide.

How F_B = qvB sin θ connects across the course

Charged particle trajectory and circular motion (Unit 12)

Because F_B is always perpendicular to v, a charge moving perpendicular to a uniform field gets bent into a circle. Set qvB equal to mv²/r and the magnetic force becomes the centripetal force. This is the single most common calculation built on this equation.

Radius of curvature and charge-to-mass ratio (Unit 12)

Solving qvB = mv²/r for r gives r = mv/qB. Heavier or faster particles trace bigger circles, and more charge or stronger field means tighter ones. Mass spectrometers exploit this to sort particles by their charge-to-mass ratio.

Velocity selector (Unit 12)

Cross an electric field with a magnetic field and balance the two forces, qE = qvB. Only particles with speed v = E/B fly through straight. It's the cleanest example of the electric and magnetic force equations working in the same problem.

Hall effect (Unit 12)

Inside a current-carrying conductor, qvB pushes the moving charges sideways until they pile up on one edge and create a voltage across the strip. The sign of that Hall voltage is classic evidence that the charge carriers are negative.

Is F_B = qvB sin θ on the AP® Physics 2 exam?

Multiple-choice questions love proportional reasoning with this equation. Double the speed, halve the field, what happens to the force? They also test the sin θ dependence, especially the trap that a charge moving parallel to B feels zero force, and the right-hand rule for direction (don't forget to reverse for negative charges). On free-response, the standard move is combining F_B = qvB with circular motion, deriving r = mv/qB or finding the period of the orbit, often inside a mass spectrometer or velocity selector setup. You should also be ready to argue in writing that the magnetic force does no work on the particle, so its speed and kinetic energy stay constant even as its direction changes. That qualitative justification shows up in paragraph-style responses.

F_B = qvB sin θ vs Electric force (F_E = qE)

Both forces act on charges, but they behave very differently. The electric force acts on any charge, moving or not, and points along the field line (or opposite it for negative charges), so it can do work and change a particle's kinetic energy. The magnetic force only acts on moving charges, points perpendicular to both v and B, and does zero work. It changes direction, never speed. In a velocity selector you set the two equal, qE = qvB, which is exactly why keeping them straight matters.

Key things to remember about F_B = qvB sin θ

• F_B = qvB sin θ gives the magnitude of the magnetic force on a moving charge, and the right-hand rule gives the direction (reversed for negative charges).

• The force is maximum when the velocity is perpendicular to the field and zero when the charge moves parallel to the field, because of the sin θ factor.

• A stationary charge experiences no magnetic force, since the equation depends on v.

• The magnetic force is always perpendicular to velocity, so it does no work and never changes the particle's speed or kinetic energy, only its direction.

• Setting qvB equal to mv²/r gives circular motion with radius r = mv/qB, the backbone of mass spectrometer and cyclotron problems.

• Balancing qE against qvB in crossed fields gives the velocity selector condition v = E/B.

Frequently asked questions about F_B = qvB sin θ

What is F_B = qvB sin θ in AP Physics 2?

It's the equation for the magnitude of the magnetic force on a moving charged object, from Topic 12.2. F_B is the force, q the charge, v the speed, B the magnetic field strength, and θ the angle between the velocity and field vectors.

Can a magnetic force change a particle's speed?

No. The magnetic force is always perpendicular to the velocity, so it does zero work and the particle's speed and kinetic energy stay constant. It only changes the direction of motion, which is why charges curve into circles in uniform fields.

How is F_B = qvB different from F = qE?

The electric force qE acts on any charge, moving or still, and points along the field, so it can speed particles up. The magnetic force qvB sin θ only acts on moving charges and points perpendicular to both v and B, so it bends paths without doing work.

Why is the magnetic force zero when a charge moves parallel to the field?

Because θ = 0° between the velocity and field vectors, so sin θ = 0 and the whole expression goes to zero. Maximum force happens at θ = 90°, when the charge cuts straight across the field lines.

How do I find the direction of the magnetic force on a charge?

Use the right-hand rule. Point your fingers along the velocity, curl them toward the magnetic field, and your thumb gives the force direction for a positive charge. For a negative charge, the force points the opposite way.