- #1
Carl140
- 49
- 0
I know that the electric potential for a continuous distributions of charge can be calculated
using the following formula:
Integral [ p(y) grad( 1/(|x-y)) d A_y ]
Where grad represents the gradient of the vector function |x-y| and A_y is a area length element and p(y) represents the charge density.
I know this result is valid for 3 dimensions.
I need the result for 2 dimensions, I remember the answer involves an expression like
grad( log(|x-y|)) where log represents the natural logarithm but I can't find it anyhwere.
Anyone knows where I can find it or how to derive it? I'm pretty sure it involves a logarithm.
I've searched in Jackson and Griffiths but couldn't find it.
Thanks in advance
using the following formula:
Integral [ p(y) grad( 1/(|x-y)) d A_y ]
Where grad represents the gradient of the vector function |x-y| and A_y is a area length element and p(y) represents the charge density.
I know this result is valid for 3 dimensions.
I need the result for 2 dimensions, I remember the answer involves an expression like
grad( log(|x-y|)) where log represents the natural logarithm but I can't find it anyhwere.
Anyone knows where I can find it or how to derive it? I'm pretty sure it involves a logarithm.
I've searched in Jackson and Griffiths but couldn't find it.
Thanks in advance