Suppose the electric field in some region is found to be E(s, Ø.2) = ks’§ where k is a constant. (a) Find the volume charge density p in this region. (b) Find the total charge contained in a cylinder of radius R, and length L that is concentric with the z-axis by integrating the charge density over the volume. (c) Use Gauss's Law to find the charge enclosed in this volume by evaluating the electric flux through the closed cylindrical surface with dimensions R and L.
Suppose the electric field in some region is found to be E(s, Ø.2) = ks’§ where k is a constant. (a) Find the volume charge density p in this region. (b) Find the total charge contained in a cylinder of radius R, and length L that is concentric with the z-axis by integrating the charge density over the volume. (c) Use Gauss's Law to find the charge enclosed in this volume by evaluating the electric flux through the closed cylindrical surface with dimensions R and L.
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Please answer (a), (b), and (c), showing all work.
Transcribed Image Text:Suppose the electric field in some region is found to be
E(s, ø,2) = ks's
where k is a constant.
(a) Find the volume charge density p in this region.
(b) Find the total charge contained in a cylinder of radius R, and length L that is concentric
with the z-axis by integrating the charge density over the volume.
(c) Use Gauss's Law to find the charge enclosed in this volume by evaluating the electric
flux through the closed cylindrical surface with dimensions R and L.
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