An ion beam has a cross-sectional of 2.5 mm^2 and the charge delivered by it to a target can be expressed as q(t)=(.12 C/s^3)t^3 + (.24 C/s^2)t^2 - .45 C. Calculate the current density in the beam at t = 3.0 seconds.

Question

I used an integral from 0 to 3s. and got 3.24C, then I inserted it to current density formula j= I/A, and I got an answer of 1296 A/m^2 and I am not sure if I'm right.

Answer 1

your procedure was correct.

Integrate? Why, all you are looking for is at time 3 .

q=.12*27+.24*9-.45 Coulombs at time=3

current density= q/area

Answer 2

Ah I see, thank you very much.