Calculate the x-component of the electric field

In summary, the conversation discusses the calculation of the x-component of the electric field produced by a uniformly distributed positive charge Q along the x-axis from x=0 to x=a, with a positive point charge q located at x=a+r on the positive x-axis. The solution involves using the equation e=kQ/R^2, where R represents the distance between the charge and the point. To integrate, the charge on a segment dx is expressed as dq=(q/a)dx, and the distance is represented as R=r+a-x and integrated from a+r to r.
  • #1
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Positive charge Q is distributed uniformly along the x-axis from x=0 to x=a. A positive point charge q is located on the positive x-axis at x=a+r, a distance r to the right of the end of Q.

Homework Statement


Calculate the x-component of the electric field produced by the charge distribution Q at points on the positive x-axis where x>a (i.e., r>0) in terms of some or all of the variables k, q, Q, a, and r, where k=\\frac{1}{4\\pi\\epsilon_0}.

The Attempt at a Solution


I'm having a problem visualizing the distance between the charge and the point. I understand that e=KQ/R^2. However, I have no idea how to get R.
I would do: (k*dQ)/(r+a-x)...
(kQ/a) [integral]1/(r+a-x)dxBut I don't think that looks right. Can anyone give me a few pointers?
 
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  • #2
Looks great! Except you forgot to square the distance (r+a-x) in the integral.
Also, something must be done about dq to express it in terms of dx so it will be possible to integrate. The charge on a segment dx would be dq = (q/a)dx because the charge per unit length is q/a.
Finally, the integral is awkward with the r and a in there. You can get it with math techniques of course (let R= r+a-x), but it might be better to think of the distance as R and integrate it from R = a+r to r. Of course dR = dx.
 
  • #3
Thank you for your help. I needed someone to confirm the distance for me since I was completely lost on that part.
 

FAQ: Calculate the x-component of the electric field

1. What is the formula for calculating the x-component of the electric field?

The formula for calculating the x-component of the electric field is Ex = (k*q*x)/r^3, where k is the Coulomb's constant, q is the charge, x is the distance from the charge to the point where the electric field is being calculated, and r is the distance between the charge and the point.

2. How is the x-component of the electric field related to the y-component?

The x-component and y-component of the electric field are perpendicular to each other, meaning they form a right angle. This means that they are independent of each other and cannot be directly related. However, both components are necessary to fully describe the electric field at a point.

3. Can the x-component of the electric field be negative?

Yes, the x-component of the electric field can be negative. This indicates that the electric field is pointing in the opposite direction of the positive x-axis. This can happen if the charge creating the electric field is negative or if the point where the electric field is being calculated is on the opposite side of the charge from the positive x-axis.

4. How does the distance from the charge affect the x-component of the electric field?

The x-component of the electric field is inversely proportional to the cube of the distance from the charge. This means that as the distance increases, the x-component decreases. This can be seen in the formula Ex = (k*q*x)/r^3, where r is in the denominator. This relationship shows that the electric field becomes weaker as you move further away from the charge in the x-direction.

5. Can the x-component of the electric field be calculated for a point inside a charged object?

No, the electric field at a point inside a charged object cannot be calculated. This is because the electric field inside a charged object is not constant and can vary depending on the distribution of charges. The formula Ex = (k*q*x)/r^3 is only valid for calculating the electric field at a point outside of a charged object.

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