Video: Finding the Current Density of an Electron Beam

An electron beam with a radius of 0.90 mm has a measured current ๐ผ = 30.00 ฮผA. What is the magnitude of the current density of the beam?

01:28

Video Transcript

An electron beam with a radius of 0.90 millimeters has a measured current ๐ผ equals 30.00 microamps. What is the magnitude of the current density of the beam?

We can name the beam radius, 0.90 millimeters, ๐‘Ÿ. And weโ€™re told the beamโ€™s measured current value 30.00 microamps. Weโ€™ll name the current density of the beam capital ๐ฝ. To get started with our solution, we can recall that current density, ๐ฝ, is equal to ๐ผ over the area over which that current is spread. In our case, the current, ๐ผ, is given. And the area over which it spread is a circular cross section of the beam with radius ๐‘Ÿ.

When we recall that the area of a circle is equal to ๐œ‹ times its radius squared, we see we can replace ๐ด in our equation, so that ๐ฝ is now equal to ๐ผ over ๐œ‹๐‘Ÿ squared. Both ๐ผ and ๐‘Ÿ are given to us. So weโ€™re ready to plug in and solve for ๐ฝ.

When we do, weโ€™re careful to use units of amperes for current and meters for our radius. When we calculate this fraction, we find that, to two significant figures, ๐ฝ is 12 amps per meter squared. Thatโ€™s the current density of the beam.

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