Magnetic Force F = qv x B: Magnitude, Direction and Angle Rule

Physics · Moving Charges And Magnetism · NEET

The magnetic force on a moving charge is F = qv x B, and its magnitude is F = qvB sin θ, where θ is the angle between velocity v and field B. The force is always perpendicular to both v and B, so it changes the direction of motion but never the speed. Memory hook: "Q-V-B, at right angles three" — F, v and B are mutually perpendicular, and the force dies out when v is along B (sin 0 = 0).
F = q v x B (magnitude F = qvB sin θ)+qvBFθθ = 90° → F = qvB (maximum)θ = 0° → F = 0 (v parallel to B)F ⟂ v and F ⟂ B (always)negative charge → F flips direction
Force F is perpendicular to both v and B. It is maximum when v is perpendicular to B (θ = 90°) and zero when v is parallel to B (θ = 0°). For a negative charge, F points the opposite way.

Your doubts, answered

When is the magnetic force zero and when is it maximum?

Force is F = qvB sin θ. It is ZERO when θ = 0° or 180° (charge moving parallel or anti-parallel to B, sin θ = 0). It is MAXIMUM (F = qvB) when θ = 90° (charge moving perpendicular to B, sin 90° = 1). A stationary charge (v = 0) also feels no magnetic force. This single rule answers most NEET one-liners.

What exactly is the angle θ in F = qvB sin θ?

θ is the angle between the velocity vector v and the magnetic field vector B, measured tail-to-tail. It is NOT the angle with any axis or with the force. Always slide the two vectors so their tails meet, then read the angle between them. If v and B are given in i, j, k form, use the cross product instead of guessing the angle.

Why is the magnetic force always perpendicular to velocity?

Because F = qv x B is a cross product, and a cross product is always perpendicular to both vectors that make it. So F ⟂ v and F ⟂ B at every instant. Since F is perpendicular to v, it can only turn the charge, not speed it up or slow it down. That is why magnetic force does no work and speed stays constant.

How do I get the direction of the force on a negative charge?

First find the direction of v x B using the right-hand rule (fingers point along v, curl toward B, thumb gives v x B). For a positive charge, F points along v x B. For a NEGATIVE charge (like an electron), F points OPPOSITE to v x B. Missing the sign flip for electrons is the most common NEET mistake.

Does the charge feel a force if it just sits in the field?

No. Magnetic force needs motion: F = qvB sin θ has v in it, so if v = 0 the force is 0. A charge must be moving (and not exactly along B) to feel a magnetic force. This is the key difference from the electric force qE, which acts even on a charge at rest.

⚠️ The NEET trap
Force is maximum when the charge moves along the magnetic field.
Force is maximum when the charge moves perpendicular (θ = 90°) to B, and ZERO when it moves along B (θ = 0°). F = qvB sin θ.
🧠 'Along B, sin 0, force gone' — parallel motion feels no magnetic force. Perpendicular gives the biggest kick.

Real NEET questions

NEET 2023 Phase 2

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron

A · Speed will decrease
B · Speed will increase
C · Will turn towards right of direction of motion
D · Will turn towards left of direction of motion
Solution: Step 1: The velocity v is parallel to B. Magnetic force F = qvB sin θ with θ = 0°, so sin 0 = 0 and the magnetic force is ZERO. No deflection from B. Step 2: Only the electric force acts. For an electron the charge is negative, so F = -eE points opposite to E. Step 3: The velocity points along E (same as the fields), so the force is opposite to the motion → the electron decelerates. Answer: speed will decrease (A). Note: because the magnetic force is zero along B, the electron does not turn at all — that rules out C and D.

Solved Moving Charges And Magnetism NEET PYQs

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Frequently asked

What is the formula for the magnetic force on a moving charge?

F = qv x B (vector form), with magnitude F = qvB sin θ, where q is the charge, v the speed, B the field and θ the angle between v and B.

What is the SI unit of magnetic field B from this formula?

From F = qvB sin θ, B = F/(qv sin θ). Its SI unit is the tesla (T), where 1 T = 1 N per (ampere·metre) = 1 kg per (C·s).

Can magnetic force change the speed of a charge?

No. Since F is always perpendicular to v, the force does no work, so kinetic energy and speed stay constant. It only changes the direction of motion.

What rule gives the direction of the magnetic force?

The right-hand rule for v x B: point fingers along v, curl toward B, thumb gives v x B. For a positive charge F is along v x B; for a negative charge it is opposite.

Is F = qvB sin θ the same as the Lorentz force?

It is the magnetic part. The full Lorentz force is F = qE + qv x B, which adds the electric force qE. When E = 0, only the qv x B magnetic part remains.