Electric Field Video Lessons

Concept

# Problem: A positive charge is located at the center of a cube. a. Are the intersections of the field lines with a side of the box uniformly distributed across that side? Explain. b. We can consider the left side of the box as composed of many small surface elements of equal area. i. Is the number of field lines through surface element A greater than, less than, or equal to the number of field lines through surface element B? Explain. ii. Is the flux through surface element A greater than, less than, or equal to the flux through surface element B? Explain. c. Consider the surface element A itself as composed of many even smaller pieces. Would the number of field lines through each of those new small surface elements vary much from one to another? Explain. Describe how the field lines for the positive point charge appear to be distributed when the region over which you look becomes sufficiently small.

###### FREE Expert Solution

Electric field:

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{q}}{{\mathbf{r}}^{\mathbf{2}}}}$, where r is the distance from the point charge q.

a.

From the electric field equation, it is clear that r varies on the same side of the cube.

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###### Problem Details

A positive charge is located at the center of a cube.

a. Are the intersections of the field lines with a side of the box uniformly distributed across that side? Explain.

b. We can consider the left side of the box as composed of many small surface elements of equal area.

i. Is the number of field lines through surface element A greater than, less than, or equal to the number of field lines through surface element B? Explain.

ii. Is the flux through surface element A greater than, less than, or equal to the flux through surface element B? Explain.

c. Consider the surface element A itself as composed of many even smaller pieces. Would the number of field lines through each of those new small surface elements vary much from one to another? Explain. Describe how the field lines for the positive point charge appear to be distributed when the region over which you look becomes sufficiently small.