C
CraftExam
medium difficulty11 min

Lorentz Force on a Moving Charge

Lorentz force is the total force on a charge q moving with velocity v in the presence of electric field E and magnetic field B, given by F = q(E + v × B).

In one line: Magnetic force turns the velocity; it does not pull along the velocity.

Concept Practice Coming Soon

Understand it

  • The electric part qE acts whether the charge is moving or at rest.
  • The magnetic part q(v × B) acts only when the charge has velocity with a component perpendicular to the magnetic field.
  • Its direction is perpendicular to both v and B, and it is reversed for a negative charge.
  • If v is perpendicular to B and there is no electric field, the magnetic force provides centripetal force, so the charge moves in a circular path.

Example

An electron entering a uniform magnetic field at right angles follows a circular path. The magnetic force changes the direction of velocity but not the speed because it is always perpendicular to the motion.

Formula and rule

F = q(E + v × B).

Magnetic force magnitude: FB = qvB sin θ.

For perpendicular entry into uniform B: qvB = mv2/r, so r = mv/(qB) using magnitude of q. q is in coulomb, v in m s−1, B in tesla, F in newton, m in kg, r in metre.

Use this when the magnetic field is uniform and motion is perpendicular to B for circular motion.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A proton of mass 1.67 × 10−27 kg and charge 1.6 × 10−19 C enters a 0.20 T magnetic field with speed 2.0 × 106 m s−1 perpendicular to the field.

  1. 1r = mv/(qB) = (1.67 × 10−27 × 2.0 × 106)/(1.6 × 10−19 × 0.20) = 0.104 m approximately.
  2. 2The proton follows a circle of radius about 10.4 cm.

Method you can reuse

  1. 1Identify q, m, v, B, and angle θ.
  2. 2Choose F = qvB sin θ for magnetic force.
  3. 3For circular motion with perpendicular entry, equate qvB to mv2/r.
  4. 4Substitute SI units.
  5. 5Decide force direction using v × B and reverse it for a negative charge.

Sketch it in your answer

Draw v tangent to the circular path, B perpendicular to the plane, and F toward the centre. Use dot for field out of page and cross for field into page. Label charge sign because force direction reverses for negative charge.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why does a charged particle moving perpendicular to a uniform magnetic field move in a circular path?

Think first, then show answer
It moves in a circular path because the magnetic force qvB is always perpendicular to its velocity and acts as the centripetal force. The force changes only the direction of motion, not the speed.

Common wrong answer

Using r = qB/(mv) reverses the formula and gives a physically wrong result, where faster particles would have smaller radius.

Don't mix this up

Students often use F = qvB even when velocity is parallel to the magnetic field. The correct form is F = qvB sin θ, so the magnetic force is zero when θ = 0 degrees or 180 degrees.

Exam tip

Always mention the angle between v and B, the sign of charge, and the direction rule. In numerical questions, use the magnitude of charge for radius and then discuss direction separately.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Usually asked as a numerical on radius or force, a direction question using right-hand rule, or an assertion-reason item on why magnetic force does no work.
  1. 1

    Enough for 1 mark

    Lorentz force is the total force on a charge q moving with velocity v in the presence of electric field E and magnetic field B, given by F = q(E + v × B).

  2. 2

    Add for 2 marks

    Example: An electron entering a uniform magnetic field at right angles follows a circular path. The magnetic force changes the direction of velocity but not the speed because it is always perpendicular to the motion.

  3. 3

    Add for 3 marks

    The electric part qE acts whether the charge is moving or at rest.

Practice

Concept practice is coming soon

Login to access concept-level MCQs and weak-concept practice as they become available.

10 MCQs5 MinutesInstant Results
Login

Help improve this page

Found something confusing, incorrect, or missing?

Open Learning Map