Magnetic Force

Fields
definition

Also known as: Lorentz force, force on a current

Grade 9-12

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The force exerted on a moving charge or current-carrying conductor by a magnetic field. The magnetic force on currents is the operating principle of every electric motor.

Definition

The force exerted on a moving charge or current-carrying conductor by a magnetic field.

💡 Intuition

A moving charge in a magnetic field feels a sideways push — perpendicular to both its motion and the field. It's like a cross-wind deflecting a moving ball.

🎯 Core Idea

Magnetic force acts perpendicular to velocity — it changes direction but not speed.

Example

A current-carrying wire between two magnets jumps sideways — this is how electric motors work.

Formula

F = qvB\sin\theta (on a charge) or F = BIL\sin\theta (on a wire of length L).

Notation

q is the charge in coulombs, \vec{v} is the velocity vector in m/s, \vec{B} is the magnetic field in tesla (T), I is the current in amperes, and L is the wire length in metres. The cross product \times gives a vector perpendicular to both inputs.

🌟 Why It Matters

The magnetic force on currents is the operating principle of every electric motor.

💭 Hint When Stuck

When solving a magnetic force problem, first identify whether it is a moving charge (F = qvB\sin\theta) or a current-carrying wire (F = BIL\sin\theta). Then find the angle \theta between the velocity (or current direction) and the magnetic field. Finally, use the right-hand rule to determine the direction of the force.

Formal View

The magnetic force on a point charge moving with velocity \vec{v} in a field \vec{B} is given by the Lorentz force law: \vec{F} = q\vec{v} \times \vec{B}. For a straight current-carrying wire of length L, the force is \vec{F} = I\vec{L} \times \vec{B}.

🚧 Common Stuck Point

The force is zero when the charge moves parallel to the field — it's maximum when perpendicular.

⚠️ Common Mistakes

  • Using the wrong angle — \theta is the angle between the velocity vector and the magnetic field, not between the force and the field.
  • Forgetting that the magnetic force is zero when the charge moves parallel to the field (\sin 0° = 0).
  • Applying the right-hand rule incorrectly for negative charges — the force direction reverses for electrons compared to positive charges.

Frequently Asked Questions

What is Magnetic Force in Physics?

The force exerted on a moving charge or current-carrying conductor by a magnetic field.

What is the Magnetic Force formula?

F = qvB\sin\theta (on a charge) or F = BIL\sin\theta (on a wire of length L).

When do you use Magnetic Force?

When solving a magnetic force problem, first identify whether it is a moving charge (F = qvB\sin\theta) or a current-carrying wire (F = BIL\sin\theta). Then find the angle \theta between the velocity (or current direction) and the magnetic field. Finally, use the right-hand rule to determine the direction of the force.

How Magnetic Force Connects to Other Ideas

To understand magnetic force, you should first be comfortable with magnetic field, electric current and force. Once you have a solid grasp of magnetic force, you can move on to motor and electromagnetic induction.

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