- #1
Phezik
Homework Statement
There is a finite line charge with length L = 1 meter and linear charge density λ = 1*10^-16 C/m. Point P is h = 70cm above the line charge and distance x from the right end of the line charge. The magnitude and direction of the electric field at point P must be found. The final answer should only contain one variable, unknown length x.
Homework Equations
Gauss's Law: ∫E*dA = Q/ε0
Trig Equations: a2+b2=c2, cosθ=adjacent/hypotenuse, sineθ=opposite/hypotenuse
Vector Equations: Magnitude of a vector E with components Ex and Ey, √(Ex2+Ey2)
The Attempt at a Solution
I set up two integrals to try to solve this problem one for each component of E, the electric field vector. Ex and Ey. Ey was setup using Gauss's law and and using hypotenuse R for the distance times cosθ to find the y competent of the electric field. The integral was then written in terms of height h and distance x and length L for the limits of integration. I then solved the integral to obtain the equation for Ey. I did an identical procedure for Ex except using sinθ to find the x component of the vector.
After finding Ex and Ey I could find E's magnitude using the formula for a vector's magnitude given it's components. I then used cotangent inverse to find the angle (and therefore the direction) of electric field vector E. I added 180° to this angle to find it's angle from the positive x axis.
My theory and execution all seemed correct when I went over it to try to find where I went wrong. I was able to successfully use the same method to find the electric field over a line charge where the point was above the middle of the finite line charge by only finding Ey as the Ex components canceled out. I'm thinking there might be an error in my vector analysis as I only had to deal with one component in the previous problem.