Electrostatics calculation help

[Fusilli_Jerry89]

Homework Statement

What is the radius of the orbit of an electron traveling at 9.0E6 m/s around a zinc nucleus(which contains 30 protons)?

Homework Equations

F=(kQq)/r^2
F=QE
ac=v^2/r
Fnet=ma

The Attempt at a Solution

30 protons x 1.6E-19 = 4.8E-18 C
electron - 1.6E-19 C

F=ma
F=(9.11E-31)a
a=v^2/r
F=[(9.11E-31)(9.0E6)^2]/r
F=7.38E-17/r
(7.38E-17/r)=[(9.0E9)(1.6E-19)(4.8E-18)]/r^2
r=9.367E-11 m

 

[Fusilli_Jerry89]

One more quick question:

I know how to prove that if you move a charge twice as far away, the force will be one forth.
[(kQq)/r^2]/[(kQq)/(2r)^2]
(KQq4r^2)/(kQqr^2)
=4 times as weak

But what about if you increase the charge by twice as much, shouldn't both charges end up being 3/2 times as strong?

[(kQq)/r^2]/[(2kQq)/r^2] I end up getting 1/2?

 

[Fusilli_Jerry89]

Qucik Question, Plz Help@@@@@

1. Homework Statement
What is the radius of the orbit of an electron traveling at 9.0E6 m/s around a zinc nucleus(which contains 30 protons)?


2. Homework Equations
F=(kQq)/r^2
F=QE
ac=v^2/r
Fnet=ma
3. The Attempt at a Solution
30 protons x 1.6E-19 = 4.8E-18 C
electron - 1.6E-19 C

F=ma
F=(9.11E-31)a
a=v^2/r
F=[(9.11E-31)(9.0E6)^2]/r
F=7.38E-17/r
(7.38E-17/r)=[(9.0E9)(1.6E-19)(4.8E-18)]/r^2
r=9.367E-11 m

One more quick question:

I know how to prove that if you move a charge twice as far away, the force will be one forth.
[(kQq)/r^2]/[(kQq)/(2r)^2]
(KQq4r^2)/(kQqr^2)
=4 times as weak

But what about if you increase the charge by twice as much, shouldn't both charges end up being 3/2 times as strong?

[(kQq)/r^2]/[(2kQq)/r^2] I end up getting 1/2?

 

[berkeman]

Okay, I unlocked your duplicate post and merged it here into this thread. Give me a minute to try to be helpful. Oh, and do not duplicate post again, okay?

 

[berkeman]

Your radius calculation looks okay. Is it not matching the solution?

 

[Fusilli_Jerry89]

i was just unsure on my answer and wanted to get it checked. Also, I am just unsure on how to prove algebraically how a difference in charge of one particle will effect the overall charge between the two, like I solved algebraically for the distance increase between the two.