Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Video: Magnetic Field of an Electromagnetic Wave

Ed Burdette

A plane electromagnetic wave travels northward. At one instant, its electric field has a magnitude of 6.0 V/m and points eastward. What is the magnitude of the magnetic field at this instant?

01:31

Video Transcript

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?

Weโ€™re told in this statement that, at one instant in time, the magnitude of the electric field is 6.0 volts per meter, which weโ€™ll call capital ๐ธ. At that same moment in time, we want to know the magnetic field, which weโ€™ll call capital ๐ต.

To begin our solution, letโ€™s recall a relationship between electric and magnetic field magnitude. At any moment in time, the magnitude of the electric field ๐ธ is equal to the magnitude of the magnetic field ๐ต times the speed of light ๐‘.

In our scenario, wanting to solve for ๐ต, we can rearrange this equation so it reads ๐ต is equal to ๐ธ divided by ๐‘, where we take ๐‘ 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 ๐ต at this moment equals 2.0 times 10 to the negative eighth tesla. Thatโ€™s the strength of the magnetic field when the electric field is 6.0 volts per meter.