Answer:
This is net charge on the surface is Q = σ₀ x (y + 2by²)
Step-by-step explanation:
The surface charge density is defined as the amount of charge Q per unit area A
σ = dq / dA
dq = σ dA
Since the surface is a rectangular region we use an xy coordinate system so the area difference
dA = dxdy
dq = σ dx dy
We replace, evaluate the integral
∫ dq = ∫ σ₀ (1 + yb) dxdy
realizamos laintegral de dx
Q -0 =σ₀ ∫ (1 + yb) (x-0) dy
Where we evaluate We must recognize that the charge Q must be zero by the time X = 0 and Y = 0. At the starting point Q = 0 for x = 0
We perform the other integral (dy)
Q = σ₀ x (y + 2y² b)
Evaluated between Y = 0 and Y = y
Q = σ₀ x (y + 2by²)
This is net charge on the surface