Physics with Calculus
Select the mathematical expression that represents electric flux through a surface in full calculus form.
A uniform electric field of magnitude EE makes a constant angle θ\(\theta\) with the normal to a flat surface of area AA. Select the expression that results from simplifying the general calculus definition of electric flux.
A rectangular panel lies in the xyxy-plane, extending from x=0x = 0 to x=Lx = L and from y=0y = 0 to y=Wy = W. The field is E⃗=(E0xL)z^\(\displaystyle\[\vec{E}\)=\(\left\)(\(\frac{E_0x}{L}\]\right\))\(\hat{z}\). Select the correct flux integral setup for the upward normal.
A rectangle has length L=3.0L=3.0 m and width W=2.0W=2.0 m, lying in the xyxy-plane with an upward normal vector. The electric field is E⃗=(12xL)z^\(\displaystyle\[\vec{E}\)=\(\left\)(\(\frac{12x}{L}\]\right\))\(\hat{z}\) N/C. Determine the electric flux through the rectangle.
Two students compute the flux through the same flat panel in the xyxy-plane. Student A chooses normal +z^+\(\hat{z}\); Student B chooses normal −z^-\(\hat{z}\). The field is E⃗=E(x)z^\(\vec{E}\) = E(x)\(\hat{z}\). Select the correct statement regarding their computed flux values.
