Magnetic Flux

Magnetic Induction

Magnetic flux

The magnetic flux is equal to the product of the magnetic field density and the surface area through which the magnetic field lines pass and which is perpendicular to the lines. If the area is not perpendicular to the lines of force, we take the component of the area that is perpendicular to the lines of force of the magnetic field.

Magnetic flux

The magnetic flux unit is:

Let's imagine that a wire loop encloses the surface area . If the magnetic flux through the loop changes with time , a voltage is induced in it. The voltage induced is given as:

If there are turns of the loop, the induced voltage is:

The magnetic flux through the loop changes if the surface or the magnetic field density changes with time - see equation (1). Therefore:

Example

The example is available to registered users free of charge.

Self induction

Let's assume we have a coil with turns and a cross-sectional area . The current through the coil changes over time . Due to the change in current, the magnetic flux through the coil also changes. The result is an induced voltage , which is calculated using equation (3) above:

 We insert the formula for Magnetic field density which is given as: and note also that only the current through the coil changes: Let's put the variables with the symbol together:

The first factor in the right-hand side of the above equation depends only on the coil itself (number of turns, area, and the substance of the coil). We call it inductance. Let us denote it by L:

The unit for inductance is (Henry):

The induced voltage can now be written in the form:

Direction of induced voltage

Why did we put a minus sign in the equation for induced voltage?

This is according to Lenz's rule which states that the direction of the induced voltage is such that the current it drives inhibits the cause of the induced voltage (change in magnetic flux).

Example

The example is available to registered users free of charge.

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