Well... if you were to move along the z-axis while keeping the same x and y coordinates, your change in voltage would be 0 since the voltage doesn't depend on z. So the line of charge would be along the z axis and just points in the \hat{k} direction, right?
Ohhhh, wait a second. I see what I'm doing now.
So by doing the gradient I got that:
Ex = -(V0x)/(x2 + y2)
Ey = -(V0y)/(x2 + y2)
Ez = 0
And if you model sqrt{x2 + y2} as a vector "r", you get that the field has an inverse dependence on r and that the object producing the field would probably...
Well I understand the idea that V(\vec{r}) varies with x and y, but isn't V0 a constant? That's what's confusing me. Generally when things have the subscript "0", they're looked at as a constant. If this is true, then how would I take the gradient of the voltage?
And when I say "In the...
Homework Statement
The space dependence of an electric potential V(\vec{r}) = V(x,y,z)=V0ln((sqrt{x2 + y2})/a)
1. What is the electric field at position \vec{r} = <x,y,z>?
2. Explain how the electric field looks in general. Make a sketch.
3. What object would produce an electric...
Okay, so I'm pretty sure I have it now:
So for the first part I got E=rρ/2ε0 in the direction of vector "r"
For the second part I got that E=0
For the third part I got that E=bρ/2ε0 in the direction of vector "r"
Does that seem right? The only thing I'm not totally sure about now is...
Well for the first part I calculated that electric field for a "r" that was greater than "R", so shouldn't it be decreasing as "r" gets greater? Instead of doing this, should I calculate the electric field at the border of the cylinder?
For the second part, well then could you explain what...
Homework Statement
A very long, solid insulating cylinder with radius "R" has a cylindrical hole with radius "a" bored along its entire length. The solid material of the cylinder has a uniform volume charge density "ρ". In this problem, you will find the magnitude and the direction of the...