Calculating Charges q_1, q_2, and q_3 with Integration

In summary, the conversation is about finding the charge q_1, q_2, and q_3 and solving a problem involving electric flux and integration. The equation used is Φ = integral (E * dA) = EA sphere and the property of adding electric flux. The solution involves writing equations for each surface and solving a system of equations with 3 unknowns, which are the charges of q_1, q_2, and q_3. The final answers are 2q, q, and -3q.
  • #1
kyang002
22
0
Question 4

What is the charge q_1?

What is the charge q_2?

What is the charge q_3?

Unsure of which equation to use, and the equations that I am looking at involve integration.

Φ = integral (E * dA) = EA sphere

Φ = q / ε

Can someone teach me how to do this problem?
 

Attachments

  • knight_Figure_27_30.jpg
    knight_Figure_27_30.jpg
    7.8 KB · Views: 357
Last edited:
Physics news on Phys.org
  • #2
HINT:Use the property of the electric flux (which is a scalar) of adding wrt the same surface.You'll have to solve a very simple system of equations...

Daniel.
 
  • #3
Property of Electric Flux = EA cos theta? But there is no theta. Unsure of the area and of the E.
 
  • #4
No.Let be [itex] \Phi_{1} [/itex] the electric flux generated by a charge [itex] q_{1} [/itex] through the (closed) surface S.Similar [itex] \Phi_{2} [/itex] for q_{2} [/itex].Then the total flux is simply the sum of Phi's which,due to the same denominator (epsilon),translates to the charges...

Daniel.
 
  • #5
So what is the charge of q_1, q_2, and q_3?

-q/E + (-2q/E) + 3q/E = 0/E = 0

The charge of each is 0?
 
  • #6
No,you have to write equations of the type phi_{1}+phi_{2}=phi_{tot} for all 3 surfaces & will end up with an algebraic system of 3 eqn. with 3 unknowns,namely the charges.

Daniel.
 
  • #7
Okay, got it. The answers are 2q, q, -3q. Am I correct?
 

1. How do you use integration to calculate charges q1, q2, and q3?

Integration is a mathematical process that allows us to calculate the area under a curve. In the context of calculating charges q1, q2, and q3, we can use integration to find the total charge by summing up the infinitesimal charges along a continuous charge distribution.

2. What is the formula for calculating charges using integration?

The formula for calculating the total charge using integration is Q = ∫q(x)dx, where Q is the total charge, q(x) is the charge density function, and dx represents the infinitesimal charge element.

3. Can you provide an example of using integration to calculate charges?

Let's say we have a linear charge distribution with a charge density function of q(x) = 2x, where x is the distance along the distribution. To find the total charge, we can integrate q(x) from 0 to 5 (the length of the charge distribution) as follows: Q = ∫0^5 2x dx = x^2 from 0 to 5 = 25 units of charge.

4. What are the units of the charges calculated using integration?

The units of the charges calculated using integration will depend on the units of the charge density function q(x). In most cases, charge density is measured in units of charge per unit length, so the units of the total charge Q will be units of charge (e.g. coulombs).

5. Are there any limitations to using integration for calculating charges?

Yes, there are some limitations to using integration for calculating charges. Integration assumes a continuous charge distribution, so it may not be accurate for systems with discrete charges. Additionally, the accuracy of the calculated charges may decrease for complex charge distributions with varying charge density functions.

Similar threads

Ranking charge stored on three capacitors by a battery
    • Introductory Physics Homework Help
Replies
6
Views
1K
Net force on a charge ##Q_3##
    • Introductory Physics Homework Help
Replies
14
Views
2K
Position of a charge (out of 3) with a net force of 0
    • Introductory Physics Homework Help
Replies
3
Views
1K
Connecting two charged capacitors in series
    • Introductory Physics Homework Help
Replies
21
Views
2K
Fourier transform of triangle diagram
    • Advanced Physics Homework Help
Replies
2
Views
250
Find Velocity of Particle for System of Charges
    • Introductory Physics Homework Help
Replies
13
Views
1K
Finding energy in a 4 object charge system
    • Introductory Physics Homework Help
Replies
7
Views
4K
Calculating the charge of two concentric conductive spheres
    • Introductory Physics Homework Help
Replies
3
Views
1K
B When a charge moves with respect to a second charge, does the electric field change?
    • Classical Physics
Replies
7
Views
621
Equivalent capacitance of a system from potential difference
    • Introductory Physics Homework Help
Replies
7
Views
6K

Hot Threads

Recent Insights

Back
Top