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[LOCK] Electric potential problem (now with TL;DR)
homeobocks
Registered User regular
Registered User regular
D'oh. I'm such a dumbass.
Imaging an electric dipole with charges +q and -q a distance d away from eachother, and a point a distance r from the dipole, equidistant to both charges.
At point P, would V = k * 2 * |q| / r (edit: r should be $ \sqrt{r^2 + d^2 / 4} $
or does V = 0 ?
Where k is the standard one over four pi epsilon.
My textbook gives the potential due to a series of point charges as V = k * (sum over n)( q_n / r_n) * which makes me think that having equal positive and negative charges equidistant from the point cancel out to zero. Which is unintuitive, and seems to contradict V's definition at P as an integral of the field vector dot ds**.
* for you native TeX readers out there, $ k \sum_n \frac{q_n}{r_n} $
** $ -\int_\infty^P E \cdot ds $
TL;DR
(a simpler problem that raises the same question) Imagine two equal and opposite point charges +/- q, and distance between them 2r. Is the potential at the point exactly between them 0 or is it k * 2q / r ? If it's zero like my textbook implies, why? There is non-zero field between them, so shouldn't a test charge placed there get kinetic energy, meaning it has potential?
Imaging an electric dipole with charges +q and -q a distance d away from eachother, and a point a distance r from the dipole, equidistant to both charges.
At point P, would V = k * 2 * |q| / r (edit: r should be $ \sqrt{r^2 + d^2 / 4} $
or does V = 0 ?
Where k is the standard one over four pi epsilon.
My textbook gives the potential due to a series of point charges as V = k * (sum over n)( q_n / r_n) * which makes me think that having equal positive and negative charges equidistant from the point cancel out to zero. Which is unintuitive, and seems to contradict V's definition at P as an integral of the field vector dot ds**.
* for you native TeX readers out there, $ k \sum_n \frac{q_n}{r_n} $
** $ -\int_\infty^P E \cdot ds $
TL;DR
(a simpler problem that raises the same question) Imagine two equal and opposite point charges +/- q, and distance between them 2r. Is the potential at the point exactly between them 0 or is it k * 2q / r ? If it's zero like my textbook implies, why? There is non-zero field between them, so shouldn't a test charge placed there get kinetic energy, meaning it has potential?
homeobocks on
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