use Gauss's law?

Question

A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of lambda, and the cylinder has a net charge per unit length of 2lambda. From this information, use Gauss's law to find (a) the charge per unit length on the inner and outer surfaces of the cylinder and (b) the electric field outside the cylinder, a distance r from the axis.

Answer 1

(a)
Inside the surface: E inside the shell is 0 (zero) so total charge inside the gaussian surface is zero so inside charge/length = -lamda
0 = (lamda)l + q{inside} => -lamda = q{inside} / l

outside the surface: total charge is 2 * lamda * l = q{in}+q{out}
q{out} = 2*lamda*l+ lamda*l = 3*lamda

(b)
E =[ 2k{e}(3 lamda) ] / r
= 6 k{e} lamda / r
= (3*lamda) / ( 2 pi epsilon{0} r) , radially outward

Answer 2

that can help you you save in ideas the distinction, bear in mind that Gauss' theorem is math and a Gauss' regulation is physics. Gauss's regulation (a "regulation" is physics-talk for equation) describes the field produced by technique of a cost. it may properly be written both contained in the fundamental or differential form. In fundamental form, it describes the flux through a closed floor, both surrounding the fee or no longer (the completed flux is 0 if the fee is outside the exterior). contained in the differential form, it describes the very undeniable truth that and electric powered field "radiates" from a cost. Gauss's theorem is the maths device to get from the fundamental type of the regulation to the differential form or vice versa. It relates the flux through a floor to the divergence of the field in a volume. again, theorem is math, regulation is physics.

Answer 3

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