Electric field of a disk & u-substitution

In summary, the electric field of a disk can be calculated using the formula E = (σ/2ε<sub>0</sub>)(1-(z/√(z<sup>2</sup>+R<sup>2</sup>)), and we use u-substitution to simplify the integration process in this calculation. The electric field of a point charge decreases with distance, while the electric field of a disk charge remains constant at a certain distance from the center of the disk. The distance from the center of the disk affects the electric field, with the electric field decreasing as the distance increases. Additionally, the electric field of a disk can be negative when the surface charge density is negative.
  • #1

Homework Statement


Calculate the electric field at point P (refer to visual):
Capture.JPG


Homework Equations


I follow everything - except how the limits of integration for the u-integral (
Capture1.JPG
) are arrived at?

The Attempt at a Solution


u=x2 is the smallest value u can have, and u=x2+R2 is the greatest value u can have?
 
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  • #2
The lower limit of the u integration should correspond to the lower limit of the r integration (r = 0). So, the lower limit of the u integration is the value of u when r = 0. Similarly for the upper limit.
 
  • #3
Very helpful - thank you!
 

1. What is the formula for calculating the electric field of a disk?

The formula for calculating the electric field of a disk is E = (σ/2ε0)(1-(z/√(z2+R2)) where σ is the surface charge density, ε0 is the permittivity of free space, z is the distance from the center of the disk, and R is the radius of the disk.

2. Why do we use u-substitution when calculating the electric field of a disk?

We use u-substitution to simplify the integration process when calculating the electric field of a disk. It allows us to substitute a more complex expression with a simpler variable, making it easier to solve the integral.

3. What is the difference between a point charge and a disk charge?

A point charge is a single point with a concentrated charge, while a disk charge is a two-dimensional object with a distributed charge. The electric field of a point charge decreases with distance, while the electric field of a disk charge remains constant at a certain distance from the center of the disk.

4. How does the distance from the center of the disk affect the electric field?

The electric field of a disk is inversely proportional to the distance from the center of the disk. This means that as the distance increases, the electric field decreases. However, when the distance is very large compared to the radius of the disk, the electric field approaches zero.

5. Can the electric field of a disk be negative?

Yes, the electric field of a disk can be negative. This occurs when the surface charge density is negative, which means that the electric field vector points in the opposite direction of the outward normal vector of the disk.

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