Electrostatics - point charges and work

In summary: Joules.In summary, to bring a 3.0 μC point charge to x = 3.0 mm, y = 0.0 mm and a 9.0 μC point charge to x = -3.0 mm, y = 0.0 mm, it would take 41 J of work, using the formula F = k(q1)(q2)/r^2 and calculating the distance between the two charges using their coordinates. This work is equal to the energy stored in the system, and thus has the same unit of Joules.
  • #1
HenryHH
12
0
Electrostatics -- point charges and work

Homework Statement



A 3.0 μC point charge and a 9.0 μC point charge are initially infinitely far apart. How much work
does it take to bring the 3.0 μC point charge to x = 3.0 mm, y = 0.0 mm and the 9.0 μC point charge to x = -3.0 mm, y = 0.0 mm? (The value of k is 9.0 × 109 N∙m2/C2.)

q1 = 3.0 uC, q2 = 9.0 uC, k = 9.0 × 109 N∙m2/C2

Homework Equations



F = k(q1)(q2)/r^2

The Attempt at a Solution



I know the answer is 41 J (this is just a practice problem). I'm assuming that the formula F = k(q1)(q2)/r^2 is supposed to be used because I have values for most variables, but I'm not sure what the radius would be. If one point charge is at x = 3mm and the other point charge is at x = -3mm, then is the radius 6 mm (I got this value by counting along the x-axis)? Also, how would the answer end up being in Joules?
 
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  • #2


When two discrete charges are brought together, the amount of work one has to do is just the energy which gets stored in the system. Energy stored for two charges is

[tex]U=\frac{k_e q_1 q_2}{r}[/tex]

where r is the distance between the two charges. Using the coordinates of the two charges given, you can find the distance between them. Since work done is same as the energy
transfer, it has the same unit as the energy
 

1. What is electrostatics?

Electrostatics is a branch of physics that studies the behavior of stationary electric charges and their interactions with other charges and with electric and magnetic fields.

2. What are point charges?

Point charges are theoretical particles with a magnitude of electric charge concentrated at a single point in space. They are used in electrostatics to simplify calculations and understand the behavior of electric fields.

3. How do point charges interact with each other?

Point charges interact with each other through the electric force, which is a force of attraction or repulsion between two charges. The magnitude of the force depends on the distance between the charges and the magnitude of their charges.

4. What is work in electrostatics?

In electrostatics, work refers to the energy required to move a charge against an electric field. It is calculated by multiplying the magnitude of the charge, the magnitude of the electric field, and the distance the charge is moved.

5. Can point charges have different signs?

Yes, point charges can have different signs, either positive or negative. Positive charges repel each other while negative charges repel each other, but positive and negative charges attract each other. This is known as Coulomb's Law.

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