- #1
Euclid
- 214
- 0
A point charge (q, mass m) is released from rest at a distance d from a grouned infinite conducting plane. How long does it take to hit the plane?
Answer pi*(d/q)*sqrt(2pi*eps m d)
This problem seemed easy to me at very, but it leads to a second order nonlinear equation
[tex]m\frac{d^2 z}{dt^2} = \frac{q^2}{16 \pi \epsilon_0 z^2}[/tex].
I tried using energy considerations to write v as v(z), I then solved for z as z(v), and integrated the above equation for v(t), putting in the limits 0 and infinity. This did not give the correct answer, although it appeared to be close. Any suggestions?
Answer pi*(d/q)*sqrt(2pi*eps m d)
This problem seemed easy to me at very, but it leads to a second order nonlinear equation
[tex]m\frac{d^2 z}{dt^2} = \frac{q^2}{16 \pi \epsilon_0 z^2}[/tex].
I tried using energy considerations to write v as v(z), I then solved for z as z(v), and integrated the above equation for v(t), putting in the limits 0 and infinity. This did not give the correct answer, although it appeared to be close. Any suggestions?