A plane electromagnetic wave travels northward. At one instant, its electric field has a magnitude of 6.0 volts per meter and points eastward. What is the magnitude of the magnetic field at this instant?
We’re told in this statement that, at one instant in time, the magnitude of the electric field is 6.0 volts per meter, which we’ll call capital 𝐸. At that same moment in time, we want to know the magnetic field, which we’ll call capital 𝐵.
To begin our solution, let’s recall a relationship between electric and magnetic field magnitude. At any moment in time, the magnitude of the electric field 𝐸 is equal to the magnitude of the magnetic field 𝐵 times the speed of light 𝑐.
In our scenario, wanting to solve for 𝐵, we can rearrange this equation so it reads 𝐵 is equal to 𝐸 divided by 𝑐, where we take 𝑐 to be exactly 3.00 times 10 to the eighth meters per second.
When we enter these values into our equation and calculate this fraction, we find that 𝐵 at this moment equals 2.0 times 10 to the negative eighth tesla. That’s the strength of the magnetic field when the electric field is 6.0 volts per meter.