Magnetic Force Formula

Magnetic force is the force exerted on a moving charge or current-carrying conductor by a magnetic field.

The Formula

F=qvBsin⁡θ (on a charge) or F=BILsin⁡θ (on a wire of length L).

When to use: 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.

Quick Example

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

Notation

q is the charge in coulombs, v⃗ is the velocity vector in m/s, B⃗ is the magnetic field in tesla (T), I is the current in amperes, and L is the wire length in metres. The cross product × gives a vector perpendicular to both inputs.

What This Formula Means

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

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.

Formal View

The magnetic force on a point charge moving with velocity v⃗ in a field B⃗ is given by the Lorentz force law: F⃗=qv⃗×B⃗. For a straight current-carrying wire of length L, the force is F⃗=IL⃗×B⃗.

Worked Examples

Example 1

easy
A proton (q=1.6×10−19 C) moves at 5×106 m/s perpendicular to a 0.3 T magnetic field. What is the magnetic force on the proton?

Answer

F=2.4×10−13 N

First step

1
Use F=qvBsin⁡θ with θ=90°.

Full solution

  1. 2
    F=1.6×10−19×5×106×0.3×1
  2. 3
    F=2.4×10−13 N
The magnetic force on a moving charged particle is perpendicular to both the velocity and the magnetic field. It causes the particle to move in a circular path rather than speeding it up or slowing it down.

Example 2

medium
A wire carrying 8 A is 0.5 m long and placed at 60° to a 0.4 T magnetic field. What force acts on the wire?

Example 3

medium
A proton (q=1.6×10−19 C) moves at 3×106 m/s perpendicular to a 0.5 T magnetic field. Find the magnetic force.

Common Mistakes

  • Using the wrong angle — θ is the angle between the velocity vector and the magnetic field, not between the force and the field. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Forgetting that the magnetic force is zero when the charge moves parallel to the field (sin⁡0°=0). - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Applying the right-hand rule incorrectly for negative charges — the force direction reverses for electrons compared to positive charges. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Using magnetic force from a keyword alone - Signal words like field, charge, magnet only point to a possible model; the system must match too.

Why This Formula Matters

Magnetic Force gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

Frequently Asked Questions

What is the Magnetic Force formula?

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

How do you use the Magnetic Force formula?

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.

What do the symbols mean in the Magnetic Force formula?

q is the charge in coulombs, v⃗ is the velocity vector in m/s, B⃗ is the magnetic field in tesla (T), I is the current in amperes, and L is the wire length in metres. The cross product × gives a vector perpendicular to both inputs.

Why is the Magnetic Force formula important in Physics?

Magnetic Force gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

What do students get wrong about Magnetic Force?

Students often know a formula related to magnetic force but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Magnetic Force formula?

Before studying the Magnetic Force formula, you should understand: magnetic field, electric current, force.

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