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Question

The electron beam in a certain cathode ray tube possesses cylindrical symmetry, and the charge density is represented by $\rho_{v}=-0.1 /\left(\rho^{2}+10^{-8}\right) \mathrm{p} \mathrm{C} / \mathrm{m}^{3}$ for $0<\rho<3 \times 10^{-4} \mathrm{m}, \text { and } \rho_{v}=0 \text { for } \rho>3 \times 10^{-4} \mathrm{m}.$ (a) Find the total charge per meter along the length of the beam; (b) if the electron velocity is $5 \times 10^{7} \mathrm{m} / \mathrm{s},$ and with one ampere defined as 1C/s, find the beam current.

Solution

VerifiedStep 1

1 of 4(a) Draw the uniform volume charge density of the electron beam, we get:

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