A charge q sits at the back comer of a cube, as shown in Fig. 2.17.What is the flux of E through the shaded side?

Short Answer

Expert verified

The electric flux through the shade area is=q24ξ0.

Step by step solution

01

Describe the given information

It is given that a charge qsits at the back comer of a cube.as shown in following figure

The flux of electric field through the shaded side need to be evaluated.

02

Define the Gauss law

If there is a surface area enclosing a volume, possessing a charge inside the volume then the electric field due to the surface or volume charge is given asE.da=qε0

Hereqis the total charge inside the volume,ε0is the permittivity of free surface.

03

Obtain the electric flux

The left side expression of the gauss law,E.da=qencosedE0, that is E.dais called the electric flux and it is equal to the quantity qenclosedε0

There are 4 cubes above the charge 2 cubes at the side of the charge, and 2 cubes below the charge. Thus there are 8 cubes in total surrounding the charge

The charge passes through each cube equally. So, the charge per face of each cube becomes 16.The 16thpart is quarter of the large cube as shown in following figure,

So, the total flux per face of each cube becomes 1614.that is 124.Thus, the flux through the shaded area is

Thus, the electric flux through the shade area is =q24ε0.

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