I did the same question with another of my class today. However, this time, this class of students had more problems in visualising why a smaller sphere having a smaller charge could possibily have a stronger electric field at the surface. I also had students who told me that their secondary school teachers told them that it was the charge per unit area that mattered and asked me how to reconcile this with the concept of electric field being stronger.
Let us address the first issue first. To aid in the visualisation. I drew the following picture. In this case, we had already made a calculation of 0.3 micro-coulomb on the small sphere and 0.9 micro-coulomb residing on the larger sphere. So if there is one electric field line drawn for each 0.1 micro-coulomb charge on it sphere, then we see can have:
So from the diagram above, we see that the although there is less charge on the smaller sphere, the electric field lines could be closer, and hence the E-field could be stronger.
Now for the second question, was the secondary teacher right in saying that it is the charge per unit area that mattered. Two ways to understand this, first the diagram shows fundamentally an essential point in drawing field lines, the no. of field lines are proportional to the charge, therefore have a greater no. of charge per unit area, essentially means more electric field lines per unit area and hence the field lines will be closer and in other word, the electric field is stronger.
Alternatively, those who prefer to see equations will have
From the equation, we can see that the electric field strength at the surface of the charged sphere can be written as a constant multiplied by (Q / surface area of sphere), so essentially the secondary teacher who relates the electric field at the surface to the Q per unit area is actually correct.
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