Download Assignment # 2 - McMaster Physics and Astronomy

Physics 2A03
Assignment #2 : Φ
1) A long, straight wire, carrying a uniform linear charge density λ, passes
through the centre of the imaginary cube shown, perpendicular to the top and
bottom faces. Find the electric flux through the shaded face in the diagram,
if λ = 100 nC/m, and the cube has side length L = 30 cm. Use Gauss’s Law,
and briefly explain your reasoning.
2) A closed surface with dimensions a = b = 0.400 m and c = 0.600 m is
located as shown below. The left edge of the closed surface is located at
position x = a. The electric field throughout the region is non-uniform and
given by E = (3ln(x) + 2x2) î N/C, where x is in meters.
a) Calculate the net electric flux leaving the closed surface.
b) What net charge is enclosed by the surface?
3) A long hollow metal cylinder has an inner radius of a and an outer radius
of b. The cylinder has an axis that coincides with that of a straight thin wire,
hence surrounding it. Given that the wire has a charge per unit length of λ,
and the cylinder has a net charge per unit length of 3λ, use Gauss’s law to
find:
a) the charge per unit length on the inner and outer surfaces of the cylinder.
b) the electric field outside the cylinder (r>b), a distance r from the axis.
4) A charge distribution with spherical symmetry has a volume density ρ v
given by:
 o r

v   R
 0
,
0rR
rR
a) Using Gauss’s law and spherical coordinates determine the electric field
everywhere.
b) Make a plot of the magnitude of the field as a function of r.
5) A volume charge density is given by ρv=rcos2θ C/m3, for a cylinder of
radius 1m with -2≤ z ≤ 2 m.
a) Use cylindrical coordinates to find the total charge enclosed.
b) Given that the electric field through the surface of this cylinder is given
by: E= (1/εo) zrcos2θ ẑ C/m2, use Gauss’s law to verify the answer in part a
above. Include a diagram, show your dA elements and explain your steps.