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

Question

2. 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.

Explanation / Answer

a)
E= K*Q/R^2

whre R is distance where we wamt to calculate the field.

Clearly R varies on the same side of cube.
So E will not be same. It won't be uniformly distributed

b)
i)Field lines through A is greater. At A R is small so, E will be large. Hence large numbers of field lines
Answer: Greater than

ii)
Flux through will be greater becuse E is greater and angle between E and area vector in case of A is 90 degree.
Answer: Greater than

c)
Since the surfaces are very small. Distance of any surface from charge will be same. So E will be same for all.

Last part:

Field lines will so close that we can cosider them as 1 line for infinitesimally small surface

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