Net Charge of Cube: -2385075 uC

[irnubcake]

Homework Statement

At each point on the surface of a cube the electric field is parallel to the z axis. The length of each edge of the cube is 3.5 m. On the top face of the cube the electric field is in the negative z direction and has a magnitude of 37 N/C magnitude. On the bottom face of the cube the field is in the positive z direction and has a magnitude of 15 N/C. Determine the net charge contained within the cube.

The Attempt at a Solution

The electric flux at the top face = EA = (-37 N/C)(3.5m)^2 = -453.25 N.m^2/C
At the bottom face = (15 N/C)(3.5m)^2 = 183.75 N.m^2/C

Gauss's law: flux * permittivity constant = charge
Applied on cube: (net flux)(permittivity constant) = net charge
(-269.5 Nm^2/C)(8.85*10^-12) = -2.385075 * 10^-9 C
= -2385075 uC (micro)
Both value and units are incorrect. > < "

 

[variation]

Hello,

Basically, you used the correct physical law.
But some mistake is done when the eletric flux was calculated.
The top surface:$$\vec{A}_t=3.5^2\hat{z}(m^2)$$ and $$\vec{E}_t=-37\hat{z}(N^2/C)$$.
The bottom surface:$$\vec{A}_b=-3.5^2\hat{z}(m^2)$$ and $$\vec{E}_b=+15\hat{z}(N^2/C)$$
You may use these quantities and try again.
Also notice the constant in Gauss's law:$$\oint\vec{E}\cdot d\vec{A}=\frac{Q_\text{total}}{\epsilon_0}$$


Goodluck

 

[m2003]

I would like to point out that the units for electric flux should be Nm^2, not Nm^2/C. Additionally, the net charge should be a positive value, as the electric field on the bottom face is in the positive z direction. Therefore, the correct calculation would be:

Electric flux at top face = (-37 N/C)(3.5m)^2 = -453.25 Nm^2
Electric flux at bottom face = (15 N/C)(3.5m)^2 = 183.75 Nm^2
Net electric flux = (-269.5 Nm^2) + (183.75 Nm^2) = -85.75 Nm^2
Net charge = (-85.75 Nm^2)(8.85*10^-12) = -7.59*10^-10 C = -759 uC (micro)

Therefore, the net charge contained within the cube is -759 microCoulombs. It is important to pay attention to units and signs when performing calculations in science, as they can greatly affect the accuracy of our results.