# The cube has edge length

The cube has edge length 1.40 m and is oriented as shown in a region of uniform electric field. Find the electric flux through the right face if the electric field, in newtons per coulomb, is given by (a)6.00$\vec i$ (b)-2.00$\vec j$ and (c)-3.00$\vec i$+$4\vec k$ (d) What is the total flux through the cube for each field?

Image from: J. Walker, D. Halliday, and R. Resnick, Fundamentals of physics: [extended], 10th ed. United States: Wiley, John & Sons, 2013.

#### Solution:

Note that when taking the dot product between unit vectors, the following rules hold:

$\vec i\cdot \vec j=\vec i\cdot \vec k=\vec j\cdot \vec k=0$

and

$\vec i\cdot \vec i=\vec j\cdot \vec j=\vec k\cdot \vec k=1$

a) $\Phi=(6.00)\vec i\cdot (1.4^2)\vec j=0$

(0 because ij=0, thus our components gets cancelled out)

b) $\Phi=(-2.00)\vec j\cdot (1.4^2)\vec j=-3.92$$\dfrac{N\cdot m^2}{C}$

c) $\Phi=(-3.00\vec i$+$4\vec k)\cdot (1.4^2)\vec j=0$

(Again, 0 because  ij=jk=0)

d)The flux is 0. Why? Remember that in a uniform electric field, the flux through a closed surface is 0.