- #1
emhelp100
- 14
- 0
Homework Statement
A point charge +Q exists at the origin. Find [itex]\oint[/itex] [itex]\vec{E} [/itex] [itex]\cdot \vec{dl}[/itex] around a square centered around the origin. I know the answer is 0, but can someone check my setup?
Homework Equations
[itex]E=\frac{Q(\vec{R}-\vec{R'})}{4\pi E_0 |\vec{R}-\vec{R'}|^3}[/itex]
The Attempt at a Solution
For E1 and E3, R = [itex]\hat{x}x+\hat{y}\frac{a}{2}[/itex] and R' = [itex]0[/itex]
E1 = E3 = [itex]\frac{Q\hat{x}x+\hat{y}\frac{a}{2}}{4\pi E_0(x^2+\frac{a^2}{4})^{3/2}}[/itex]
dl1=dl3 = [itex]\hat{x}dx[/itex]
E2=E4=[itex]\frac{Q\hat{x}\frac{a}{2}+\hat{y}y}{4\pi E_0(y^2+\frac{a^2}{4})^{3/2}}[/itex]
dl2=dl4 = [itex]\hat{y}dy[/itex]