Lorentz Force: Force on a Moving Charge in Electric and Magnetic Fields
Physics · Moving Charges And Magnetism · NEET
The Lorentz force is the total force on a moving charge when both an electric field E and a magnetic field B are present: F = qE + q(v x B), or F = q(E + v x B). The electric part qE acts along E and can change the particle's speed; the magnetic part q(v x B) is always perpendicular to velocity, so it only bends the path and never changes speed. Memory hook: "E for energy (speed), B for bend (turn)."
The Lorentz force splits into two parts: qE points along E and changes the charge's speed (red), while q(v x B) is always perpendicular to v and only bends the path (green). When v is parallel to B, the magnetic part is zero.
Your doubts, answered
Does the magnetic part of the Lorentz force ever change the speed of a charge?
No. The magnetic force q(v x B) is always at 90 degrees to the velocity v, so it does zero work (W = F.v = 0). It can only change the direction of motion, not the speed or kinetic energy. Only the electric part qE can speed up or slow down the charge.
What happens if the velocity v is parallel to B?
Then v x B = 0, so the magnetic force is zero and the charge moves straight through the magnetic field as if it were not there. This is exactly why in NEET 2023 an electron shot along both E and B fields only feels the electric force and simply slows down (or speeds up), with no turning.
Why does qE change speed but q(v x B) does not?
qE points along the field E, so it usually has a component along v, meaning it does work and changes kinetic energy. q(v x B) is built from a cross product, so it is always perpendicular to v; a force perpendicular to motion does no work and cannot change speed.
When is the net Lorentz force on a moving charge zero?
When the electric force exactly cancels the magnetic force: qE = q(v x B) in magnitude and opposite in direction. For perpendicular E, v and B this gives E = vB. The charge then moves in a straight line with no deflection. This is the velocity selector idea used in NEET 2025.
For an electron, does the force point along E or opposite to E?
Opposite. The charge of an electron is negative (q = -e), so the electric force F = qE = -eE points opposite to E. Always plug the sign of the charge into F = q(E + v x B); do not just use the field direction.
⚠️ The NEET trap ✗ Assuming the magnetic field slows the electron down because it 'pushes' on it. ✓ The magnetic force q(v x B) is perpendicular to v, so it does no work and cannot change speed; only qE changes speed. When v is along B, the magnetic force is even zero. 🧠 Ask first: is the force along v (changes speed) or perpendicular to v (only turns)? B always turns, never speeds up.
Real NEET questions
NEET 2023
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: Velocity v is parallel to B, so the magnetic force = q(v x B) = 0 (angle 0, sin 0 = 0). No turning from B. Step 2: Only the electric force acts. For an electron q = -e, so F = qE = -eE, which points opposite to E. Step 3: Since v is along E, this force is opposite to v, so it decelerates the electron. Result: speed will decrease. Answer: A.
NEET 2025
An electron (mass 9 x 10^-31 kg, charge 1.6 x 10^-19 C) moving with speed c/100 is injected into a magnetic field B of magnitude 9 x 10^-4 T perpendicular to its motion. We apply a uniform electric field E together with B so that the electron does not deflect. Then (c = 3 x 10^8 m/s):
A · E parallel to B, magnitude 27 x 10^2 V/m
B · E parallel to B, magnitude 27 x 10^4 V/m
C · E perpendicular to B, magnitude 27 x 10^4 V/m
D · E perpendicular to B, magnitude 27 x 10^2 V/m ✓
Solution: Step 1: For zero deflection the electric force must cancel the magnetic force: qE = qvB, so E = vB. Step 2: The magnetic force q(v x B) is perpendicular to both v and B, so E must be perpendicular to B to oppose it. Step 3: v = c/100 = 3 x 10^8 / 100 = 3 x 10^6 m/s; B = 9 x 10^-4 T. Step 4: E = vB = (3 x 10^6)(9 x 10^-4) = 27 x 10^2 V/m. So E is perpendicular to B with magnitude 27 x 10^2 V/m. Answer: D.
Solved Moving Charges And Magnetism NEET PYQs
Try the real previous-year questions from this chapter — each with the answer and a full solution.
F = qE + q(v x B) = q(E + v x B), where q is the charge, E the electric field, v the velocity and B the magnetic field. It is the total force on a charge from both fields together.
Is the Lorentz force a vector or a scalar?
It is a vector. Its direction depends on the field directions, the velocity direction and the sign of the charge. You add the electric part and the magnetic part as vectors.
What is the direction of the magnetic part of the Lorentz force?
It is perpendicular to both v and B, given by the right-hand rule for v x B, then reversed if the charge is negative. Its magnitude is qvB sin(theta), where theta is the angle between v and B.
Can the Lorentz force be zero even when the charge is moving?
Yes. If qE and q(v x B) cancel (E = vB with correct directions), the net force is zero and the charge moves in a straight line. This is the basis of the velocity selector.
Why is the Lorentz force important for NEET?
It is the parent formula for the whole chapter: velocity selectors, cyclotrons, circular and helical motion, and force on wires all come from F = q(E + v x B). Knowing which part changes speed and which part only turns solves many one-line questions fast.
