Gauss Law

Given data:

• Side length of the cube, cm m
• Magnitude of electric field through surface ABCD, N/C
• Magnitude of electric field through surface EFGH, N/C
• Permittivity of free space, F/m

Using Gauss's Law, the total electric flux through the Gaussian surface is equal to the total charge enclosed divided by the permittivity of free space:

The electric flux through a surface is given by:

Since the electric field lines are parallel to the x-axis, the angle between the electric field and the normal to the surfaces ABCD and EFGH is and respectively. Therefore, and .

The area of each face of the cube is:

The electric flux through surface ABCD is:

The electric flux through surface EFGH is:

The total electric flux through the Gaussian surface is the sum of the fluxes through all surfaces. Since the electric field lines are parallel to the x-axis, the flux through the other four faces is zero. Therefore, the total flux is:

Using Gauss's Law, the total charge enclosed by the cube is:

Therefore, the total charge enclosed by the cube is .