Question

A cylindrical beam of electric charge flows with uniform velocity u⃗ =10z^ [m/s] The beam's axis is the z^-axis, and it has a radius of r=0.8 [meters] and it has a charge density of rhov=−3r2 [C/m3] Calculate the net electric charge flux (the net current) flowing in the +z^-direction through the z=0 plane. Give the answer in units of [A]. Give three significant figures.

Answer 1

Answer:

Net electric charge flux is 19.30.

Explanation:

Velocity u =10 z

Charge density ,ρv = - 3r²

r= 0.8 m

The net electric charge given as

$n.e.c.=\oint \rho_v.u.ds$

u .ds= 10 dA

Now by putting the values

$n.e.c.=\int_{0}^{2\pi}\int_{0}^{0.8}-3r^2.10r.dr.d\theta$

$n.e.c.=-30\int_{0}^{2\pi}\int_{0}^{0.8}r^3dr.d\theta$

$n.e.c.=2\pi\left(\dfrac{30r^4}{4}\right)_0^{0.8}$

$n.e.c.=2\pi\left(\dfrac{30\times (0.8)^4}{4}\right)$

n.e.c=19.30

So the net electric charge flux is 19.30.