An electric field is E = sign(x 360 N/C?, where sign x equals-i îfx 0 0 ifx and
ID: 2034102 • Letter: A
Question
An electric field is E = sign(x 360 N/C?, where sign x equals-i îfx 0 0 ifx and +1 fx > O A cylinder or i ength L : 16 cm and radius. R at the origin and its axis along the x axis such that one end is at x= +8 cm and the other is at x =-8 cm 3 3 m has ts enter (a) What is the flux through each end? N m2/c (+x end) N m2/c (-x end) (b) What is the flux through the curved surface of the cylinder? (c) What is the net outward flux through the entire cylindrical surface? N m2/c (d) What is the net charge inside the cylinder?Explanation / Answer
electric flux = E.A
(a)
flux through end at x = 8 cm = 0.08 m
Area of cross section = pi*R^2 = pi*0.033^2 = 0.0034 m^2
area vector is along -i
flux = -360 i . 0.0034 (-i) = 1.224 N .m^2/C <<-------ANSWER
flux through end at x = -8 cm
Area of cross section = pi*R^2 = pi*0.033^2 = 0.0034 m^2
area vector is along i
flux = 360 i . 0.0034 (i) = 1.224 N .m^2/C <<-------ANSWER
(b)
normal to the curved surface is in yz plane
the angle between normal and Electric field = 90
flux = E.A = E*A*cos90 = 0 <<-------ANSWER
(c)
net flux = 1.224 + 1.224 = 2.448 Nm^2/C <<-------ANSWER
(d)
total flux = qnet/e0
net charge = qnet = 2.448*8.84*10^-12 = 21.6*10^-12 C <<-------ANSWER
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