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How to Calculate Force from Magnetic Field Strength?

Published in Electromagnetism 4 mins read

The force exerted on a charged particle moving in a magnetic field is calculated using the Lorentz force equation, considering the charge, velocity, magnetic field strength, and the angle between the velocity and magnetic field vectors.

Here's a breakdown of how to calculate the magnetic force:

Understanding the Lorentz Force

The Lorentz force describes the combined force on a charged particle due to electric and magnetic fields. In the context of solely a magnetic field, the equation simplifies to:

F = qvB sin θ

Where:

  • F is the magnetic force (measured in Newtons, N)
  • q is the electric charge (measured in Coulombs, C)
  • v is the velocity of the charge (measured in meters per second, m/s)
  • B is the magnetic field strength (measured in Teslas, T)
  • θ (theta) is the angle between the velocity vector (v) and the magnetic field vector (B)

Steps to Calculate Magnetic Force

  1. Identify the known values: Determine the charge (q), velocity (v), magnetic field strength (B), and the angle (θ) between the velocity and magnetic field.
  2. Ensure consistent units: Make sure all values are in the standard units (Coulombs, meters per second, Teslas, and degrees or radians, respectively).
  3. Calculate sin θ: Find the sine of the angle between the velocity and magnetic field vectors. If the velocity and magnetic field are perpendicular, θ = 90°, and sin θ = 1.
  4. Apply the formula: Plug the values into the formula F = qvB sin θ to calculate the magnitude of the magnetic force.
  5. Determine the direction: Use the right-hand rule to determine the direction of the force. Point your fingers in the direction of the velocity (v), curl them towards the direction of the magnetic field (B), and your thumb will point in the direction of the force (F) for a positive charge. If the charge is negative, the force direction is opposite to the direction your thumb points.

Example

Let's say you have an electron (q = -1.6 x 10-19 C) moving at a velocity of 2 x 106 m/s perpendicular (θ = 90°) to a magnetic field of 0.5 T.

  1. q = -1.6 x 10-19 C
  2. v = 2 x 106 m/s
  3. B = 0.5 T
  4. θ = 90° , sin θ = 1

Applying the formula:

F = (-1.6 x 10-19 C) (2 x 106 m/s) (0.5 T) * 1 = -1.6 x 10-13 N

The magnitude of the force is 1.6 x 10-13 N. The negative sign indicates that, due to the negative charge of the electron, the direction of the force is opposite to what the right-hand rule would initially suggest.

Important Considerations

  • Velocity is Key: If the charge is stationary (v = 0), the magnetic force is zero, regardless of the magnetic field strength.
  • Direction Matters: The magnetic force is strongest when the velocity is perpendicular to the magnetic field (sin 90° = 1) and zero when the velocity is parallel to the magnetic field (sin 0° = 0).
  • Right-Hand Rule: Accurately applying the right-hand rule is crucial for determining the force's direction. Remember that the direction is reversed for negative charges.

In summary, calculating the magnetic force requires knowing the charge, its velocity, the magnetic field strength, and the angle between the velocity and the magnetic field. Applying the Lorentz force equation (F = qvB sin θ) and understanding the right-hand rule will allow you to accurately determine both the magnitude and direction of the force.

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