Magnetic Force Calculator

Understanding Magnetic Force Calculator

The Lorentz force on a moving charge in a magnetic field is perpendicular to both the velocity and the field direction (right-hand rule).

How to use this calculator

1. Enter the charge value, \(q\), in coulombs.
2. Enter the speed of the charge, \(v\), in meters per second.
3. Enter the magnetic field strength, \(B\), in teslas.
4. Enter the angle \(\theta\) between the velocity and the magnetic field, then calculate.

The formula explained

The formula \(F = qvB\sin\theta\) computes the magnetic force on a moving charge. It tells you how strong the force is based on the charge, its speed, the magnetic field, and the angle between the motion and the field.

• F = magnetic force in newtons
• q = charge in coulombs
• v = speed of the charge in meters per second
• B = magnetic field strength in teslas
• \(\theta\) = angle between the velocity and the magnetic field

Step by step method

1. Write down \(q\), \(v\), \(B\), and \(\theta\).
2. Find \(\sin\theta\).
3. Multiply \(q\), \(v\), \(B\), and \(\sin\theta\) to get \(F\).

Worked example

Problem. A charge of \(2\ \text{C}\) moves at \(3\ \text{m/s}\) through a magnetic field of \(4\ \text{T}\) at an angle of \(30^\circ\). Find the magnetic force.

1. Use \(F = qvB\sin\theta\).
2. Substitute the values: \(F = 2 \times 3 \times 4 \times \sin 30^\circ\). Since \(\sin 30^\circ = \frac{1}{2}\), this becomes \(F = 2 \times 3 \times 4 \times \frac{1}{2}\).
3. Compute the result: \(F = 12\ \text{N}\).

Tips and common mistakes

• If the angle is \(0^\circ\), the force is \(0\) because \(\sin 0^\circ = 0\).
• Make sure the angle is the one between the direction of motion and the magnetic field, not just any angle in the problem.

Frequently asked questions