Electrostatics calculation help

In summary, the radius of the orbit of an electron traveling at 9.0E6 m/s around a zinc nucleus with 30 protons is 9.367E-11 m. To prove that moving a charge twice as far away results in one fourth the force, you can use the equation [(kQq)/r^2]/[(kQq)/(2r)^2] and simplify to get a result of 1/4. However, to prove the effect of a difference in charge, you need to use the equation [(kQq)/r^2]/[(2kQq)/r^2] and simplify to get a result of 1/2.
  • #1
Fusilli_Jerry89
159
0

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
 
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  • #2
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?
 
  • #3
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?
 
  • #4
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?
 
Last edited:
  • #5
Your radius calculation looks okay. Is it not matching the solution?
 
  • #6
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.
 

What is electrostatics calculation?

Electrostatics calculation is the process of using mathematical equations and principles to determine the behavior and properties of electrically charged particles and objects.

What are the basic principles of electrostatics?

The basic principles of electrostatics include Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Other principles include the concept of electric fields and potential, as well as the conservation of charge.

How do you calculate the electric field of a charged object?

The electric field of a charged object can be calculated using the equation E = F/q, where E is the electric field, F is the force exerted on the object, and q is the magnitude of the charge. This equation can be further modified for different scenarios, such as point charges or charged plates.

What is the difference between electrostatics and electrodynamics?

Electrostatics deals with the study of stationary electric charges and their behavior, while electrodynamics involves the study of moving charges and how they interact with each other and with electromagnetic fields.

What are some real-world applications of electrostatics?

Electrostatics has many practical applications, including in the design of electronic devices, such as capacitors and transistors. It is also used in particle accelerators, air purifiers, and electrostatic precipitators for air pollution control. Additionally, electrostatics plays a role in many industrial processes, such as painting, coating, and printing.

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