### Video Transcript

An electron beam with a radius of 0.90 millimeters has a measured current ๐ผ 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. And weโre told the beamโs measured current value 30.00 microamps. Weโll name the current density of the beam capital ๐ฝ. To get started with our solution, we can recall that current density, ๐ฝ, is equal to ๐ผ over the area over which that current is spread. In our case, the current, ๐ผ, is given. And the area over which it spread is a circular cross section of the beam with radius ๐.

When we recall that the area of a circle is equal to ๐ times its radius squared, we see we can replace ๐ด in our equation, so that ๐ฝ is now equal to ๐ผ over ๐๐ squared. Both ๐ผ and ๐ are given to us. So weโre ready to plug in and solve for ๐ฝ.

When we do, weโre 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, ๐ฝ is 12 amps per meter squared. Thatโs the current density of the beam.