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How Do You Find Magnetic Flux?

Published in Electromagnetism 2 mins read

Magnetic flux is found by calculating the magnetic field strength multiplied by the area through which the magnetic field lines pass, and also considering the angle between the magnetic field and the area.

Here's a breakdown:

Understanding Magnetic Flux

Magnetic flux (Φ or ΦB) represents the amount of magnetic field passing through a given area. It's a crucial concept in electromagnetism, particularly when discussing Faraday's Law of Induction.

Formula for Magnetic Flux

The general formula for magnetic flux is:

Φ = B ⋅ A = BAcos(θ)

Where:

  • Φ is the magnetic flux (measured in Webers, Wb)
  • B is the magnetic field strength (measured in Tesla, T)
  • A is the area through which the magnetic field passes (measured in square meters, m2)
  • θ (theta) is the angle between the magnetic field vector and the normal (perpendicular) vector to the area.

Steps to Calculate Magnetic Flux

  1. Determine the Magnetic Field (B): Find the magnitude of the magnetic field strength at the location of interest. This value is usually given in Tesla (T).

  2. Determine the Area (A): Calculate the area that the magnetic field is passing through. Ensure that the area is in square meters (m2). For example, if you have a circular loop, the area would be πr2, where 'r' is the radius of the loop.

  3. Determine the Angle (θ): Find the angle between the magnetic field vector and the normal to the surface area. If the magnetic field is perpendicular to the surface, then θ = 0°, and cos(0°) = 1. If the magnetic field is parallel to the surface, then θ = 90°, and cos(90°) = 0, meaning there is no flux.

  4. Apply the Formula: Plug the values of B, A, and θ into the formula Φ = BAcos(θ) to calculate the magnetic flux.

Example

Let's say you have a circular loop with a radius of 0.1 meters in a uniform magnetic field of 20 Tesla. The magnetic field is perpendicular to the plane of the loop (θ = 0°).

  1. B = 20 T
  2. A = πr2 = π(0.1 m)2 = 0.0314 m2
  3. θ = 0° so cos(θ) = 1
  4. Φ = BAcos(θ) = (20 T)(0.0314 m2)(1) = 0.628 Wb

Therefore, the magnetic flux through the loop is 0.628 Webers.

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