Spring constant with point charges

In summary, the spring constant with point charges refers to the stiffness of a spring-like system influenced by electrical charges. It is calculated by dividing the force by the displacement and is affected by factors such as distance, charge magnitude, and dielectric constant. The spring constant is directly related to Coulomb's law and has various applications in physics and engineering.
  • #1
mujadeo
103
0

Homework Statement


Two charges Qa = 3 µC and Qb = -3 µC are placed on the x-axis with a separation of a = 21 cm.

(a) Find the net electric field at point P, a distance d = 13 cm to the left of charge Qa.

This is no prob = -1364069.13N

(b) Find the force on Qb due to Qa .

No prob again = -1.837



The charges Qa and Qb are now attached to the ends of a spring whose unstretched length is s0 = 21 cm. With the charges attached, the spring compresses to an equilibrium length s1 = 9 cm.

(c) Calculate the spring constant ks of the spring.

this is what i can't figure out?





Homework Equations





The Attempt at a Solution



heres are the steps i did (its wrong though)

1. Spring constant is Fsp = -k delta s

2. i already know the force that the 2 charges exert on each other (= 1.837N)

3. delta s would be 21cm - 9cm = 12cm = .12m

4. then i just plugged in:
1.837 = -k(.12m)
k = -15.308

this is wrong.
please help
 
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  • #2
For a) the units of E field strength are not N. For b) that looks right, except you forgot to include the units, which are Newtons. For c) figure out the potential energy stored in the compressed spring and equate it to the change of potential energy of the moved charges. You can't assume that the force is a constant.
 
  • #3
Dont I need the spring constant to get the PE stored in the spring though?
PE (in spring) = ( 1/2 k (delta s)^2)
 
  • #4
The change in the PE of the charges gives you the change in the PE of the spring. That gives you the spring constant.
 

1. What is the definition of spring constant with point charges?

The spring constant with point charges refers to the measure of stiffness of a spring-like system that is influenced by the electrical charges of two or more particles. It is a measure of the force required to stretch or compress the spring-like system by a certain distance in the presence of the point charges.

2. How is the spring constant with point charges calculated?

The spring constant with point charges is calculated by dividing the force acting on the system by the displacement of the spring-like system. This can be represented by the equation k = F/x, where k is the spring constant, F is the force, and x is the displacement.

3. What factors affect the spring constant with point charges?

The spring constant with point charges is affected by several factors including the distance between the point charges, the magnitude of the charges, and the dielectric constant (a measure of a material's ability to store electrical energy) of the medium between the charges. The geometry of the system and the material properties of the spring-like system can also impact the spring constant.

4. How does the spring constant with point charges relate to Coulomb's law?

The spring constant with point charges is directly related to Coulomb's law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The spring constant can be seen as a measure of the proportionality constant between force and distance in this equation.

5. What are some real-world applications of the spring constant with point charges?

The spring constant with point charges has various applications in physics and engineering, such as in the design of electrical circuits, in the study of atomic and molecular interactions, and in the development of microelectromechanical systems (MEMS). It is also utilized in fields like nanotechnology, biophysics, and material science to understand and manipulate the behavior of particles and materials at the molecular level.

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