Electric Field of a Solid Ball of Uniform Charge Density

In summary, E(r) represents the electric field due to a charged ball throughout all of space, and statements about E(0), E(Rb), and the maximum electric field at different distances are true. E(r) is defined as the same as a point charge for distances greater than the radius of the charged ball.
  • #1
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Homework Statement


Let E(r) represent the electric field due to the charged ball throughout all of space. Which of the following statements about the electric field are true?

- E(0) = 0
- E(Rb) = 0
- lim(r -->infin.)E(r) = 0
- The maximum electric field occurs when r = 0.
- The maximum electric field occurs when r = Rb.
- The maximum electric field occurs as r -->infin..


2. Relevant material
A solid ball of radius Rb has a uniform charge density rho .

3. Attempt at a Solution
The true statements that i chose were E(0) = 0, lim(r -->infin.)E(r) = 0, The maximum electric field occurs when r = Rb.
 
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  • #2
...attempt at solution?
 
  • #3
Your answers are correct.
 
  • #4
thank you
 
  • #5
how would u definte E(r) at distance r > rb?
 
  • #6
For r>r_b, E is the same as a point charge.
 

1. What is an electric field?

An electric field is a physical field that is created by electrically charged particles. It is a vector field, meaning it has both magnitude and direction, and it describes the force that a charged particle would experience if placed within the field.

2. How is the electric field of a solid ball of uniform charge density calculated?

The electric field of a solid ball of uniform charge density can be calculated using the formula E = kQr/R³, where k is the Coulomb's constant, Q is the total charge of the ball, r is the distance from the center of the ball, and R is the radius of the ball.

3. Does the electric field inside a solid ball of uniform charge density vary?

No, the electric field inside a solid ball of uniform charge density is constant at all points. This is because the charge is evenly distributed throughout the ball, resulting in a uniform electric field.

4. How does the electric field outside the solid ball of uniform charge density differ from the inside?

Outside the solid ball of uniform charge density, the electric field varies with distance and follows the inverse-square law. This means that the strength of the electric field decreases as the distance from the center of the ball increases.

5. What is the significance of the electric field of a solid ball of uniform charge density?

The electric field of a solid ball of uniform charge density is important in understanding and predicting the behavior of charged particles within an electric field. It also has practical applications in various fields such as electronics, electromagnetism, and energy production.

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