Uniform line of charge and point charge

In summary, the conversation discussed finding the x- and y-components of the electric field at a specific point due to an infinite line charge and a point charge. The solution involved using the equations for electric flux and electric field, and taking into account the direction and magnitude of the charges. Numerical results were obtained and checked using WolframAlpha. The final answers for the x- and y-components were -9545.026 kN/C and -4164.957 kN/C, respectively.
  • #1
noagname
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5

Homework Statement


An infinite line charge of uniform linear charge density lambda = -3.1 mu or micro CC/m lies parallel to the y-axis at x = -1 m. A point charge of 0.7 mu or micro CC is located at x = 2.5 m, y = 3.5 m. Find the x- and y-components of the electric field at x = 3.5 m, y = 3.0 m.

Homework Equations


flux = E*A = Q/ε
E = kQ/r^2

The Attempt at a Solution


X axis:
To find the electric field from the line only: gaussian cylinder, centered on the line and r = 4.5m.
E*2∏*4.5*L = λL/ε -> E1 = λ/(ε*9*∏) to the left

From the point:
E2 = K(.7*10^-6)/1.25*sin(63.43°) to the right

Ex = E2-E1 Right?

Y axis:
The line don't matter because it cancels itself out. right?
Ey = K(.7*10^-6)/1.25*cos(63.43°) Down

Both answers need to be in kN/C, I'm at a loss, do you guys have any ideas? I have tried many different answers and I've checked all of the units.
 
Last edited:
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  • #2
Your work looks good to me. What did you get for your final answer?
 
  • #3
What are your numerical results?

ehild
 
  • #5
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  • #6
Welp, I just found my mistake. Damn Radians!
 

1. What is a uniform line of charge?

A uniform line of charge is an infinite line of charge with a constant charge density along its length. This means that the amount of charge per unit length remains the same along the entire line.

2. How is the electric field calculated for a uniform line of charge?

The electric field at a point near a uniform line of charge is calculated using the Coulomb's law equation, where the distance from the point to the line of charge is used as the distance between the two point charges.

3. What is the difference between a uniform line of charge and a point charge?

A uniform line of charge has a constant charge density along its length, while a point charge has a single point of charge. Additionally, the electric field from a uniform line of charge varies with distance, while the electric field from a point charge varies with the inverse of the distance squared.

4. How does the electric field from a point charge change with distance?

The electric field from a point charge decreases with the inverse of the distance squared. This means that as the distance from the point charge increases, the strength of the electric field decreases.

5. Can a uniform line of charge and a point charge exist together?

Yes, a uniform line of charge and a point charge can exist together in the same system. In fact, the electric field produced by a point charge can be used to calculate the electric field produced by a uniform line of charge when the point charge is located at a specific distance from the line of charge.

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