The magnetic force is the force experienced by a charged particle moving through a magnetic field. This force plays a crucial role in many applications, from the design of electric motors to the movement of charged particles in plasma physics.

In this guide, we’ll explain how to calculate the magnetic force and provide a calculator to make the process easier.

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What is Magnetic Force?

The magnetic force is the force that a magnetic field exerts on a moving charge. The formula to calculate this force is derived from Lorentz force, which combines both electric and magnetic forces. The magnetic force experienced by a charged particle moving through a magnetic field is given by:

F = q * v * B * sin(θ)

Where:

• F = Magnetic force (in Newtons, N)
• q = Charge of the particle (in Coulombs, C)
• v = Velocity of the particle (in meters per second, m/s)
• B = Magnetic field strength (in Teslas, T)
• θ = Angle between the velocity vector and the magnetic field vector

Important Notes:

• If the angle (θ) between the velocity and the magnetic field is 90 degrees (perpendicular), then sin(θ) = 1, and the magnetic force will be at its maximum.
• If the particle moves parallel to the magnetic field (θ = 0 degrees), the magnetic force is zero because sin(0) = 0.

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Example Calculation

Let’s say we have a proton (charge = +1.6 × 10⁻¹⁹ C) moving with a speed of 2 × 10⁶ m/s through a magnetic field with a strength of 0.5 T. The angle between the velocity and the magnetic field is 90°.

1. Charge (q) = 1.6 × 10⁻¹⁹ C
2. Velocity (v) = 2 × 10⁶ m/s
3. Magnetic Field (B) = 0.5 T
4. Angle (θ) = 90°

The magnetic force can be calculated as:

F = q * v * B * sin(θ)

Since sin(90°) = 1:

F = (1.6 × 10⁻¹⁹) * (2 × 10⁶) * (0.5) * (1)

F = 1.6 × 10⁻¹⁹ * 10⁶

F = 1.6 × 10⁻¹³ N

So, the magnetic force is 1.6 × 10⁻¹³ N.

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Magnetic Force on a Current-Carrying Wire

If the charge is in the form of a current-carrying wire rather than a single particle, the formula for the magnetic force changes to:

F = I * L * B * sin(θ)

Where:

• F = Magnetic force (in Newtons, N)
• I = Current in the wire (in Amperes, A)
• L = Length of the wire in the magnetic field (in meters, m)
• B = Magnetic field strength (in Teslas, T)
• θ = Angle between the current direction and the magnetic field

Example Calculation for a Wire:

Consider a wire carrying a current of 3 A with a length of 0.5 m in a magnetic field of 2 T. The angle between the wire and the magnetic field is 90°.

1. I = 3 A
2. L = 0.5 m
3. B = 2 T
4. θ = 90°

The magnetic force is:

F = I * L * B * sin(θ)

Since sin(90°) = 1:

F = 3 * 0.5 * 2 * 1

F = 3 N

So, the magnetic force on the wire is 3 N.

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Magnetic Force Calculation Table

For quick reference, here’s a table for different values of the angle (θ) between the velocity/current and magnetic field:

Angle (θ)	sin(θ)	Maximum Force Condition
0°	0	No magnetic force
30°	0.5	Reduced force
45°	0.707	Moderate force
60°	0.866	Large force
90°	1	Maximum force

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FAQ: Common Questions About Magnetic Force

Q: What happens if the angle between the magnetic field and the velocity is 0° or 180°?
A: If the angle is 0° or 180°, the particle’s velocity is either parallel or anti-parallel to the magnetic field, meaning the magnetic force is zero because sin(0°) = sin(180°) = 0.

Q: Can the magnetic force change the speed of a moving particle?
A: No, the magnetic force does not do work on the particle, so it does not change the speed. It only changes the direction of motion, causing circular or spiral trajectories (such as in a cyclotron).

Q: How does the magnetic force affect a current-carrying wire?
A: The magnetic force acts on the moving charges inside the wire (the current), causing the wire to experience a force. This is the principle behind electric motors and generators.

Q: What is the difference between magnetic force and electric force?
A: The electric force acts on charged particles regardless of their motion, whereas the magnetic force only affects moving charged particles. The electric force is based on Coulomb’s law, and the magnetic force is based on the Lorentz force law.

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Magnetic Force Calculator

To help you calculate the magnetic force for different scenarios, you can use the following inputs:

1. For a moving charged particle:
   • Enter the charge of the particle (q) in Coulombs (C).
   • Enter the velocity (v) of the particle in meters per second (m/s).
   • Enter the magnetic field strength (B) in Teslas (T).
   • Enter the angle (θ) between the velocity and magnetic field in degrees.
2. For a current-carrying wire:
   • Enter the current (I) in Amperes (A).
   • Enter the length of the wire (L) in meters (m).
   • Enter the magnetic field strength (B) in Teslas (T).
   • Enter the angle (θ) between the current direction and the magnetic field in degrees.

Once you have these values, you can plug them into the formulas provided above to calculate the magnetic force.

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Conclusion

Magnetic force is a fundamental concept in electromagnetism, and understanding how to calculate it is important for a wide range of applications in physics, engineering, and technology. Whether you’re calculating the force on a moving particle or a current-carrying wire, using the right formula and understanding the role of the angle between the velocity and magnetic field are key to getting the correct result.

By using the provided formulas and examples, you can easi