E Field from Distribution of Charge

In summary, the rod has a non-uniform charge per unit length of λ(x) = A x2 where A = 3 µC/m3, where x is measured in meters from the origin. For a rod with length L = 2.9 m, the net charge on the rod is Q = 2.439e-5. To find the net x-, y-, and z-components of the electric field at the origin, we must integrate the contribution of each section of the rod to the electric field at the origin. Each section has a positive charge and is a distance x from the origin, therefore producing a leftwards force on a positive test charge at the origin
  • #1
r34racer01
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A thin rod of length L has a non-uniform charge per unit length λ(x) given by

λ(x) = A x2 where A = 3 µC/m3

and x is measured in meters from the origin.

(a) Find the net charge on the rod for L = 2.9 m.
Q = 2.439e-5

(b) Find the net x-, y-, and z-components of the electric field at the origin.
Ex = ?
Ey = 0N/C
Ez = 0N/C

HELP: Draw a diagram showing the contribution dE to the electric field at the origin produced by the infinitesimal amount of charge between x and x + dx. Check that your diagram shows the correct direction of dE.
HELP: Write down an integral expression that follows from your diagram and perform the necessary integration. Check that your expression has an overall algebraic sign that corresponds to the vector in your diagram.


So the first part was easy I just had to integrate the function given. But w/ part b I'm at a loss. I really don't understand why the net x component at the origin isn't zero. I tried integrating like the help said and I got E = (2Kλ)/y and I don't see how that helps, if I put 0 in for y that's obviously impossible. Can someone explain this and give me some hints on how to do this?
 
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  • #2
Every part of the rod has a positive charge. The entire rod is to the right of the origin, so eacht part of the rod will produce a leftwards force on a positive test charge at the origin. So the electric field at the origin can't be 0.

What is the charge of the section of the rod between x and x + dx ?

How far is this section from the origin?

What is the contribution of this section to the electric field at the origin (Coulombs law)

now integrate this over the length of the rod
 

What is an "E Field"?

The "E Field" stands for electric field and it is a physical quantity that describes the magnitude and direction of the force that a charge experiences in the presence of other charges. It is a vector field, meaning that it has both magnitude and direction at every point in space.

How is an E Field created?

The E Field is created by the distribution of electric charges. When charges are placed in a certain arrangement, they create an electric field that permeates the space around them. The strength and direction of the E Field is determined by the quantity and location of the charges.

What is the relationship between E Field and distribution of charge?

The E Field and the distribution of charge are directly related. The E Field is created by the distribution of charge, meaning that the arrangement of charges determines the strength and direction of the E Field. Changes in the distribution of charge can lead to changes in the E Field.

How is the E Field calculated from the distribution of charge?

The E Field can be calculated using Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. By using this law and considering the distribution of charges, the E Field at a specific point can be calculated.

What are some real-life applications of the E Field from distribution of charge?

The E Field has many real-life applications, including the functioning of electronic devices such as computers and cell phones, the attraction and repulsion of magnets, and the creation of lightning during thunderstorms. It is also used in medical imaging techniques such as electrocardiograms and electroencephalograms.

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