 #1
Callumnc1
 880
 103
 Homework Statement:

Four identical particles, each having charge ##q## and mass ##m##,
are released from rest at the vertices of a square of side ##L##.
How fast is each particle moving when their distance from
the center of the square doubles?
 Relevant Equations:

##U_E = qV ##
##KE = \frac{mv^2}{2} ##
I tried solving the problem above by using conservation of energy
##U_{Ei} = U_{Ef} + KE ##
##\frac{4k_eq^2}{\sqrt{2}L} = \frac{4k_eq^2}{2\sqrt{2}L} + 4(\frac{mv^2}{2}) ##
##\frac{2k_eq^2}{\sqrt{2}L} = 2mv^2 ##
## v = \sqrt {\frac {k_eq^2}{\sqrt{2}Lm}} ##
However, the solutions solved the problem differently
Would anybody please tell me what I have done wrong?
Many thanks!
##U_{Ei} = U_{Ef} + KE ##
##\frac{4k_eq^2}{\sqrt{2}L} = \frac{4k_eq^2}{2\sqrt{2}L} + 4(\frac{mv^2}{2}) ##
##\frac{2k_eq^2}{\sqrt{2}L} = 2mv^2 ##
## v = \sqrt {\frac {k_eq^2}{\sqrt{2}Lm}} ##
However, the solutions solved the problem differently
Would anybody please tell me what I have done wrong?
Many thanks!