- #1
Ashu2912
- 107
- 1
Hey friends, I am stuck up in the derivation of the electric potential energy due to a charge 'Q' at the origin on test charge 'q' at a point p (position vector 'rp'). The derivation is shown below, am just struggling with a minus sign...
Electric Potential Energy at P
= Work done to move 'q' from infinity to P quasi-statically by external agent
=[tex]\int[/tex] kQq/r2 -r[tex]\wedge[/tex].-dr
(Since External Force = - Coulumbic Force and displacement vector = -dr)
=kQq [-1/r][tex]\infty[/tex]rp
=-kQq/r
I know that when Qq is +ve, work done should be positive, but the sign is changing due to the integral.
NOTE : all vectors shown in bold faces, r^ is unit vector along r and dr is infinitesimal displacement in direction of r...
Electric Potential Energy at P
= Work done to move 'q' from infinity to P quasi-statically by external agent
=[tex]\int[/tex] kQq/r2 -r[tex]\wedge[/tex].-dr
(Since External Force = - Coulumbic Force and displacement vector = -dr)
=kQq [-1/r][tex]\infty[/tex]rp
=-kQq/r
I know that when Qq is +ve, work done should be positive, but the sign is changing due to the integral.
NOTE : all vectors shown in bold faces, r^ is unit vector along r and dr is infinitesimal displacement in direction of r...