How Do You Calculate Electric Flux Through a Circular Disk in an Electric Field?

[Physicus2]

Homework Statement

"Given a constant electric field E = E(subscript 0)(1 / square root of 2 i + 1 / square root of 2 k), find the electric flux through a circular disk of radius a lying flat in the x-y plane. Orient the disk so that the positive direction is toward positive z.

Homework Equations

The most relevant equation to this problem is Eflux = integral of E dot dA.

The Attempt at a Solution

I've completely finished a solution, but there are many places to make mistakes here, I think, despite what may be a simple problem.

I said that Eflux = (-E subscript 0) double integral from 0 to a (x and y) of E dot k dx dy. I went on to place 1 / square root of 2 into the integral, but only once for the k and not the i component. Would this be correct? I then integrated with respect to x and got (1 / square root of 2)x dy. Integrating again, I think I get (1 / square root of 2)a^2. Note that i replaced x with a there. I'm unsure if I did my double integral correctly...I'm only beginning Calculus 3 now, and it wasn't a prerequisite for Physics. Oh well.

When all is said and done, I get -E(subscript 0) a^2 / square root of 2.

Is my answer close? I presumed that E is negative because the disk was in the positive Z direction. I apologize for the fact that I'm unable to upload images of my work. Any help would be very much appreciated!

 

[mukundpa]

Is the field is uniform?

if no then think of integration.

if yes, no need of integration simply write field and the area as vectors and perform dot product of them.

 

[m2003]

As a scientist, it is important to double check your work and make sure all calculations are correct. In this case, it seems that you have correctly applied the relevant equation for electric flux and have correctly integrated with respect to x and y. However, it is important to note that in this problem, the electric field is not constant, as it varies with position. Therefore, the electric flux through the circular disk will also vary with position on the disk. It would be helpful to draw a diagram and label the electric field vectors at different points on the disk to better understand how the electric flux varies.

Additionally, it is important to pay attention to units and make sure they are consistent throughout your calculations. In this problem, the units for electric field are typically measured in N/C, while the units for electric flux are typically measured in Nm^2/C. Make sure to convert appropriately if necessary.

Lastly, it is always helpful to check your answer by plugging it back into the original equation for electric flux and making sure it satisfies the given electric field and disk dimensions. If the answer does not match, it is important to go back and review your calculations to find where the mistake was made.

Overall, it seems that you have a good understanding of the concept of electric flux and have correctly applied the relevant equations. Just make sure to double check your work and pay attention to details, such as units, to ensure accuracy in your calculations.