Of all of the electromagnetic laws, Faraday's law is by far the easiest. In order to fully understand , you must first understand some very basic geometry.

Magnetic flux is basically the product of magnetic field strength and area. Magnetic flux is measured in a unit called a weber (Wb), which is equivalent to a tesla meter squared (Tm²). For example, if we were to have an area 1 m² perpendicular to a uniform magnetic field of 1 T, then that area would have a magnetic flux of 1 Wb. Now, suppose that the shape is a triangle that is 4 m high and 2 m wide, that is perpendicular to a 1.5 T magnetic field. The area of this triangle would be 4 m² (A = ½bh = ½ * 4 m * 2 m). Therefore the flux would be F = BA cos q = 1.5 * 4* cos 0º = 6 Wb. In this formula, q represents the angle between the area vector A and the magnetic field B.

One interesting thing about magnetic flux is that it is always conserved. If you were to have a box 1 m to a side inside of a uniform magnetic field of 1 T, then one side would have 1 Wb going into one side, and 1 Wb going out of the other.

In all of these examples, I have assumed that the area in question was perpendicular to the magnetic field. What if it isn’t? In that case, you just have to take the component of the magnetic field that is perpendicular to the area. So if you have a 1m² area that forms a 30° angle with a uniform 1 T magnetic field, what is the flux? The component of the magnetic field that is perpendicular to the area is 1 T sin 30° or 0.5 T. So, the magnetic flux through this area would be 0.5 Wb.

Faradays law involves the change of flux divided by the change in time. Since flux is the product of magnetic field with incident magnetic field, there are two ways that magnetic flux may change; either the magnetic field changes, or the area changes.

Assuming that the area is constant, a changing magnetic field would create an electric field around it. Let’s pretend that we have a loop that is 1m in radius, and a magnetic field that is increasing at a rate of 1 T/s. This loop will have an area of πm², so the change in flux over change in time is pWb/s. So the Electric field multiplied by the loop is equal to pNm/C. Divide by the distance, and you find that the electric field along the path is equal to 0.5 N/C. Lets try this again, except this time the radius is 3 m, and the magnetic field is increasing at a rate of 5 T/s. The area is 9 pm², so the flux change is 45 pWb/s. The circumference is 6 pm, so the electric field is 7.5 N/C.

Now what if the magnetic field stays the same, but the area changes? Let’s suppose that there are two parallel bars of iron. They are connected at one end by a resistor, and at the other end by a slideable piece of metal. If the two bars are 1 m apart, the piece of metal slides at a rate of 1 m/s, and the uniform magnetic field is 1 T, what is the electric field across the resistor? First, since one piece has been specified as the resistor, all of the electric field goes across that resistor. When we multiply the width by the speed, we get 1 m²/s. Multiplied by the magnetic field, we get 1 Wb/s, which is the rate of . Divide 1 Wb/s by the length of the resistor (1 m), we get a uniform electric field across the resistor of 1 N/C. Let’s try something a little more advances. This time, the bars are 1.5 m wide, the speed of the piece of metal is 2 m/s, and the field strength is 5T. The rate of area change is 2 m/s*1.5 m = 3 m²/s. Therefore, the rate of change of flux is 15 Wb/s. Divided by the distance of the resistor (1.5 m), then we find that the electric field across the resistor is 10 N/C.

The biggest application of Faradays law involves the fact that is equal to voltage. So of any loop with any geometry, is equal to voltage around that loop. One important thing to deal with when looking at this voltage is Lentz’s law. This law sates that the current induced in a loop by Faradays law must act to oppose the change in the magnetic field that created it. To do this, you just need to remember the right hand rule.

It is often difficult to create a constantly changing magnetic field, and equally so for a loop whose area changes. However, it is possible to change the flux in yet another way. If the loop were to spin inside of a uniform magnetic field, then it would create an alternating voltage. Let us take a loop with an area of A, inside a magnetic field with strength B, and turning with a speed of ω. Taking one half of Faradays law, we get

 .

Since , voltage across the loop is -ABωcosθ.

Contributed by Lawrence Camarota, August 2004