Electric Field: Vector Field Integration Over a Line Charge Source
Consider a charged rod of length
b
with uniform charge density
Q/b
, as shown in the figure. Find the electric field E
x
(x) and E
y
(x) for points along the x-axis.
QUESTIONS
(Score is number right minus number wrong.)
Which is the correct substitution for the charge density in Equation (2)?
Equation (3a)
Equation (3b)
Equation (3c)
Which is (are) the correct substitution(s) for expressing the field point and source point in Cartesian coordinates?
Equation (4a) and Equation (4b) are correct
Equation (4a) only is correct
Equation (4b) only is correct
Which is correct?
The "wavy r" unit vector (normalized to unit length from Equation (1)) is a constant and can be brought outside the integral of Equation (2).
Cartesian unit vectors cannot be brought outside the integral either.
The Cartesian unit vector along the x-axis can be brought outside the integral, but the Cartesian unit vector along the y-axis cannot because the integration is along the y-axis.
Cartesian unit vectors can both be brought outside the integral because they are constant, but "wavy r" cannot.
E
x
(x) is given by expressing the integral in terms of Cartesian unit vectors and finding the coefficient of the x-unit vector. When I do that, E
x
(x) is given by
Equation (6a)
Equation (6b)
Neither
EQUATIONS
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