A flat 1.0m^2 surface is vertical at x=2.0m and parallel to the yz-plane. What is the flux through the surface if it is located in a uniform electric field given by E= 26.0i + 42.0j + 62.0k N/C?
Explanation if possible :)
what is area*E dot (1i)?
remember the directional vector of area is pependicular to the plane
So you have to do a dot product? why would it be (1i)?
To find the flux through the given surface, we can use the formula:
Flux (Φ) = ∫∫ E · dA
Where E is the electric field vector and dA is the differential area vector.
First, let's find the normal vector to the surface. Since the surface is vertical and parallel to the yz-plane, the normal vector will be in the x-direction. Therefore, the normal vector is N = i.
Now, let's find the area of the surface. The surface is given as a flat 1.0m^2 surface, which means the area A = 1.0m^2.
Using the formula, we have:
Φ = E · A
Plugging in the values:
E = 26.0i + 42.0j + 62.0k N/C
A = 1.0m^2
Let's calculate the dot product:
E · A = (26.0i + 42.0j + 62.0k) · (1.0i)
= 26.0(1.0) + 42.0(0) + 62.0(0)
= 26.0 N/C
Therefore, the flux through the surface is 26.0 N/C.