I posted a question on here earlier but I wasn't able to solve from what the person had told me.
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.
I was given a couple link to how to deal with things but I have some questions.
The line infinite line charge equation I saw gave the formula Ez=lambda/(2*pi*epslion naught*z) or with an r in place of z; but since my charge is parallel to the y-axis and
x=0 its at the origin (I think) and so I'm unsure of what distance I need. It seems like the line charge has neither an x or y charge.
Is it the distance to the point charge? If its the distance to the axes then I'm dividing by zero either way.
Also, as for direction, its positive to negative right? So the direction for adding vectorially is from the point charge to the line charge (to the left)?
Please help and thank you again.
To find the electric field at a point due to a line charge, we can use the formula you mentioned: Ez = lambda / (2 * pi * epsilon_0 * z). Here, lambda is the linear charge density, epsilon_0 is the permittivity of free space, and z is the distance from the line charge to the point where we want to find the electric field.
In your case, the line charge is parallel to the y-axis and located at x = 0 m. The point where you want to find the electric field is at x = 3.5 m, y = 3.0 m. Since the line charge is parallel to the y-axis and located at x = 0 m, the distance we need to consider is the distance between the line charge and the y-coordinate of the point we are interested in. In this case, the distance is simply 3.0 m.
So, the formula for the electric field component in the z-direction becomes Ez = lambda / (2 * pi * epsilon_0 * 3.0 m).
Regarding the direction of the electric field, it points away from positive charges and towards negative charges. In this case, since the line charge has a negative charge density and the point charge is positive, the electric field will point from the point charge towards the line charge (opposite to the direction of the vector joining them).
To find the x- and y-components of the electric field, we need to consider the components of the distance between the point charge and the point where we want to find the electric field. In this case, the x-component is 3.5 m (the distance between the point charge and the x-coordinate of the point we are interested in), and the y-component is 0 m (since the point is at the same y-coordinate as the point charge).
Now, we can calculate the magnitude and direction of the electric field. Substituting the values into the formula, we have:
Ez = -2.5 micro C / (2 * pi * epsilon_0 * 3.0 m)
To add the x- and y-components of the electric field, we need to consider their magnitudes and directions. The magnitude of the electric field along the z-direction can be determined using the formula above. For the x- and y-components, since the distance in the y-direction is 0 m, the electric field components will be zero.
Finally, to get the net electric field, we can add the x- and y-components of the electric field vectorially by taking their vector sum.
I hope this explanation helps you to solve the problem! Let me know if you have any further questions.