An infinite line charge of uniform linear charge density lambda = -2.5 micro Coulombs lies parallel to the y axis at x = 0 m. A point charge of 3.5 micro Coulombs 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.
So I get what this is asking; you have to point charges with locations given; what is the charge of the third at another given location. What I'm *not* sure of is what equations/approach to use.
I don't want to throw anyone under the bus (knowledge of the material is my responsibility) but my prof. just kinda mumbles and points at PowerPoint slides with a laser pointer so I don't have anything from my lecture to help with this. Any assistance would be much obliged; thank you in advance.
You have the electric field at (3.5,3) due to a line charge.
Then you have the electric field at (3.5,3) due to a point charge
You add those vectorialy to get the total E vector at (3.5,3)
Do that by adding the Ey components due to each
and then the Ey components due to each.
It only asks for those components, not the magnitude and direction.
The E field due to a line charge is in your text.
The E field due to a point charge is in your text.
I will see if I can find something online, but I am sure you have those.
in both cases we are talking about Coulomb's law E = k Q/r^2
Above I mean find Ex and Ey, not Ey and Ey (typo)
by the way k = 9*10^9 N m^2/C^2
To find the x- and y-components of the electric field at the given point (x = 3.5 m, y = 3.0 m), we can use the principle of superposition. The electric field at the given point is the vector sum of the electric fields due to the infinite line charge and the point charge.
Let's start by calculating the electric field due to the infinite line charge. The electric field at a point due to an infinite line charge can be calculated using the formula:
E = (lambda / (2πε₀r)) * (cosθ1 - cosθ2)
where:
- E is the electric field
- lambda is the uniform linear charge density
- ε₀ is the permittivity of free space (ε₀ = 8.854 x 10^-12 C^2/(N m^2))
- r is the distance between the line charge and the point where you want to find the electric field
- θ1 and θ2 are the angles made by the line charge with respect to the line connecting the line charge and the point where you want to find the electric field. θ1 and θ2 can be calculated using trigonometry.
For the given point (x = 3.5 m, y = 3.0 m), the distance from the point to the line charge is r = 3.5 m - 2.5 m = 1.0 m. The line connecting the line charge and the point makes an angle θ1 with the positive x-axis and an angle θ2 with the negative x-axis. Since the line charge is parallel to the y-axis, θ1 = -θ2.
To find the angles, we can use the tangent function:
tan(θ1) = y / x = 3.0 m / 1.0 m
θ1 = arctan(3.0)
Now we can calculate the electric field due to the line charge:
E_line = (lambda / (2πε₀r)) * (cosθ1 - cosθ2)
Next, let's calculate the electric field due to the point charge. The electric field due to a point charge can be calculated using Coulomb's law:
E_point = (k * q) / r²
where:
- E_point is the electric field due to the point charge
- k is Coulomb's constant (k ≈ 8.99 x 10^9 N m^2 / C^2)
- q is the charge of the point charge
- r is the distance between the point charge and the point where you want to find the electric field
For the given point (x = 3.5 m, y = 3.0 m), the distance from the point charge is r = √((3.5 m - 2.5 m)² + (3.0 m - 3.5 m)²). The charge of the point charge is q = 3.5 μC.
Now we can calculate the electric field due to the point charge:
E_point = (k * q) / r²
Finally, we can add the x- and y-components of the electric fields due to the line charge and the point charge separately to get the total electric field at the given point:
E_total_x = E_line_x + E_point_x
E_total_y = E_line_y + E_point_y
where E_line_x, E_line_y, E_point_x, and E_point_y are the x- and y-components of the electric fields due to the line charge and the point charge, respectively.
I hope this explanation helps you in solving the problem. Let me know if you have further questions!