Electric Field at Ro, Phi, and Z Help

In summary, we are given a point charge of 2[\muC] located at A(4,3,5) in free space. To find E\rho, E\phi, and Ez at P(8,12,2), we need to start in rectangular coordinates and convert to cylindrical coordinates. The R vector and |R| can be found using known formulas. No integration is needed. The magnitude and direction of E can be determined using the components Ex, Ey, and Ez. The directions of eρ and eφ can also be determined.
  • #1
akhdz
1
0
A 2[[tex]\mu[/tex]C] point charge is located at A(4,3,5) in free space. Find E[tex]\rho[/tex], E[tex]\phi[/tex], and Ez at P(8,12,2).

I know I have to start off in rectangular, convert to cylindrical coordinates. I know how to find the R vector and |R|.

Since it says there is a point charge, do I need to integrate anything? How would I find the 3 different components?
 
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  • #2
Welcome to PF!

Hi akhdz! Welcome to PF! :smile:

(have a mu: µ and a rho: ρ and a phi: φ :wink:)
akhdz said:
A 2[[tex]\mu[/tex]C] point charge is located at A(4,3,5) in free space. Find E[tex]\rho[/tex], E[tex]\phi[/tex], and Ez at P(8,12,2).

I know I have to start off in rectangular, convert to cylindrical coordinates. I know how to find the R vector and |R|.

Since it says there is a point charge, do I need to integrate anything? How would I find the 3 different components?

(No, no integration needed.)

What is the magnitude and direction of E?

What are Ex Ey and Ez ?

What are the directions of eρ and eφ ? :smile:
 

FAQ: Electric Field at Ro, Phi, and Z Help

What is an electric field?

An electric field is a physical quantity that describes the influence that a charged particle has on other charged particles in its vicinity. It is a vector field, meaning that it has both magnitude and direction.

How is the electric field at a point defined?

The electric field at a point is defined as the force per unit charge that a test charge would experience if placed at that point. Mathematically, it is represented as E = F/q, where E is the electric field, F is the force, and q is the test charge.

What is the significance of Ro, Phi, and Z in the electric field at Ro, Phi, and Z?

Ro, Phi, and Z are cylindrical coordinates used to describe the position of a point in three-dimensional space. In the context of an electric field, Ro represents the distance from the origin, Phi represents the angle from a reference direction, and Z represents the height above or below a reference plane.

How is the electric field at a point calculated using Ro, Phi, and Z?

The electric field at a point can be calculated using the formula E = kQ/r^2, where k is the Coulomb constant, Q is the charge at the source, and r is the distance from the source to the point. For cylindrical coordinates, the distance r can be calculated using the equation r = √(Ro^2 + Z^2).

What are some real-world applications of understanding the electric field at Ro, Phi, and Z?

Understanding the electric field at a point can help in the design and operation of electrical systems, such as power grids and electronic circuits. It is also important in fields such as electrostatics, electromagnetism, and particle physics. Additionally, it has applications in medical imaging, such as in MRI machines, and in technologies like touchscreens and sensors.

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