Which region (or regions) carries a net charge of the greatest magnitude?

Since all field lines are going out from (iii) so the net flux is largest in this case. In case (i) and (ii) some of the field lines are going in while others are going out so that the net flux which is a quantitative measure of the total number of field lines is less in these cases. In fact in case (ii) the net flux is zero because equal numbers of field lines are going in and out. From Gauss’s law, the net flux is equal to net charge enclosed divided by ε0 so the net charge enclosed is largest in case (iii) and zero in case (ii).

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