What Is the Magnetic Constant and Why Does It Matter?

This means these 3 values can’t beryllium independent; if you cognize 2 of them, you tin deduce the third. How bash physicists woody with this? We specify the velocity of airy arsenic precisely 299,792,458 meters per second. (How bash we cognize it’s exact? Because we specify a metre arsenic the region airy travels successful 1/299,792,458 of a second.) Then we measurement the magnetic changeless (μ₀) and usage that worth on with the velocity of airy to cipher the electrical changeless (ε₀).

Maybe that seems similar cheating, but to adjacent commencement doing existent science, astatine immoderate constituent we person to marque up arbitrary units and specify immoderate parameters. In fact, erstwhile you travel down to it, each systems of measurement are made up, conscionable similar each words are made up.

Permeability of Free Space

Magnetic fields (represented by the awesome B) tin beryllium created by magnets, arsenic shown successful the photograph up top. But due to the fact that of that interdependence we talked about, they tin besides beryllium made by moving electrical charges. (I’m utilizing the shorthand word “charges” for charged particles, similar electrons.) This is described by the Biot-Savart law:

You tin spot the magnetic changeless (μ₀) successful there. We besides person the worth of the electrical complaint (q) moving with a definite velocity (v). So this says the magnetic tract increases with the electrical complaint and decreases with the region (r) from the moving charge—and the magnetic changeless tells america precisely however overmuch it varies.

Of course, we don’t woody with idiosyncratic moving electrons precise often. But we woody with streams of moving electrons each the time: That’s electrical current, which we tin measure. If we cognize the complaint connected the particles successful coulombs, past the fig of coulombs flowing per 2nd gives america the existent (I) successful amperes. And we tin constitute the equation supra successful presumption of current: B = μ₀I/(2πr).

It’s Everywhere

What this tells america is that electric existent generates a magnetic field. This is utilized successful each kinds of machines. For instance, it gives america electromagnets, wherever the magnetic unit tin beryllium turned connected and disconnected to determination metallic objects successful factories and scrapyards. It’s besides however audio speakers make sound: An electrical awesome vibrates a magnetic driver, which generates unit waves successful the air.

Also magnetic fields power electrical currents. This is however motors work. There's a existent moving done a coil of ligament successful the beingness of a magnetic tract that's usually created with immoderate imperishable magnets. The unit connected the coil of ligament causes it to turn, and there's your motor. It could beryllium a instrumentality motor, portion of your AC compressor, oregon the main thrust for an electrical car.

Wait! There's more. Just arsenic a changing electrical tract creates a magnetic field, a changing magnetic tract creates an electrical field—and that produces an electrical current. This is however astir of our powerfulness is generated. Some vigor source—steam, wind, moving water, whatever—spins a turbine that rotates a coil wrong a magnetic field. The changing magnetic flux induces a voltage successful the coil, converting mechanical vigor into electrical vigor that tin beryllium transmitted to your home.

Measuring the Magnetic Constant

How tin we measurement μ₀? One method uses what’s called a existent balance. A elemental mentation of this has 2 parallel wires carrying electrical existent (I) successful other directions, arsenic shown successful the diagram below. Then you suspend the 2 wires with strings truthful that they tin determination apart, similar this:

The existent successful each ligament creates a magnetic tract astatine the determination of the different wire, and this pushes them apart. As they determination away, the magnetic unit decreases and the horizontal constituent of the hostility successful the enactment drawstring increases (because of the alteration successful angle). Once these 2 forces are equal, the wires volition beryllium “balanced.”

If you cognize the worth of the electrical existent and the region betwixt the wires (r), you tin find the magnetic constant, μ₀. Then, arsenic we showed above, you tin usage this worth on with the defined velocity of airy to cipher the electrical constant, ε₀.

So yeah, each successful all, you could accidental the magnetic changeless is beauteous important. Oh, and what is that changeless value? According to the International Committee for Weights and Measures, μ₀ = 1.256637061272 × 10^–6 N/A². No more, nary less.