Question

Suppose we've managed to set up an electric field that can be described by the functionE=<w1*y^2,w2z^2,w3x^2> where w1=11N(Cm2) , w2=9N(Cm2) , and w3=12N(Cm2) . Let's look at a rectangular box in the Cartesian coordinate axes, shown below, with dimensions a=15 m along the x-axis, b=7 m along the y-axis, c=35 m along the z-axis.

What is the magnitude of the electric flux passing through the shaded area?

Answer 1

Net elctric field at a distance b units on the y axis.

We have x component = 11b^2 N/C

y component = 9z^2 where z changes from 0 to C

and z component = 12 x^2 where x changes from 0 to a

But flux is integral( E.ds)

so surface has normal in y direction we just need y component only

So it is 9z^2 * a * dz since area of rectangle is length *breadth and on length side field is not changing

So if we integrate we get flux = (9z^3)/3 * a where z varies from 0 to c

So net flux = 3 ac^3.

Substitute a and c we get 3 * 1.5 * 3.5^3 = 192.9375