2m 4 meters In the figure above is shown a cylindrical Gaussian surface with a r

Question

2m 4 meters In the figure above is shown a cylindrical Gaussian surface with a radius of 2 meters and a length of 4 meters. The left surface of the cylindrical surface lies on the x-z plane at y-0 and is centered on the y- axis. The electric field in the region is given as E. Note: You should be able to provide numerical answer for all of these questions however be sure to sufficiently show your work as you are being graded on the process, not the answer. a) what is the electric flux through the surface on the x-z plane at y=0 (the left surface)? b) What is the electric flux through the Surface on the x-z plane at ye4 (the right surface)? c) What is the electric flux through the curved surface along the y-axis? d) How much charge is enclosed by this surface?

Explanation / Answer

Given

electric field is along y direction with E= 4 i +(y-1)j + 8 k N/C

cylindrical Gausssian surface with radius 2m

and length is l = 4 m

we know that the flux through a surface of area A is

flux phi = (1/epsilon not) Q_in = E*A cos theta

where theta is the angle between the electric field and normal to the surface

a) electric flux phi = E*A cos theta= E*A cos 0 = E*A

A is pi*r^2 = pi*2^2 = 4pi

phi = (4 i +(y-1)j + 8 k )(4pi) = 16 pi i - 4pi j * 32 pi k

the magnitude is phi = 113.09 Nm2/C

b) flux will be same on right side also =113.09 Nm2/C

c) curved surface along the y-axis is zero because theta is 90 degrees

d) charge enclosed by the surface is

flux = Qin/epsilon not

Q in = flux*epsilon not

= 113.09*8.854*10^-12 C

= 1 nC

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