6. (a) By Eq. 24-18, the change in potential is the negative of the“area”under the curve. Thus, using the area-of-a-triangle formula, we have VEdsx−=−⋅==z101222002GGbgbgwhich yields V= 30 V. (b) For any region within 03<< − ⋅zxEdsm,GGis positive, but for any region for which x> 3 m it is negative. Therefore, V = Vmaxoccurs at x= 3 m. dsx−=z101232003GGbgwhich yields Vmax= 40 V.
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