goober
- 1
- 0
Homework Statement
Find an equation for the net electric field at a point, above and between, two infinite line charges, one with line charge density λ and the second with line charge density -λ. The point is a distance R from both line charges, a distance y above the midpoint between charges, and the distance between charges is 2x. For reference, if the lines are viewed as parallel to the z-axis in an xy-plane, the line charges and the point would form a triangle with base 2x and height y.
Homework Equations
##\vec E## = (λ / 2π∈0r)##\hat r## (line charge field from Gauss's Law)
##\hat r## = ##\vec r## / r
R = (x2 + y2)1/2
The Attempt at a Solution
##\vec E##1 = (λ / 2π∈0R) [ (x##\hat i## + y##\hat j##) / R ]
##\vec E##2 = (-λ / 2π∈0R) [ (-x##\hat i## + y##\hat j##) / R ]
##\vec E##net = ##\vec E##1 + ##\vec E##2 = 2xλ / 2π∈0R2##\hat i## = (xλ / π∈0R2)##\hat i##
I found the electric field for each line charge individually using the equation given in the textbook for Gauss's law on an infinite line charge. I then added the two field vectors and found a final result where the y-components canceled and the x-components doubled. I just need to know if this is the correct method for solving the problem, because I was led to believe it would be more complex.