An electric field in a given region of space is given by
E=3.1x2i
(in N/C). What is the magnitude of the potential difference between
two points x=0 m and x=7.5 m, i.e. |V(x=7.5m)-V(x=0 m
)|?
\(E = -\frac{dV}{dx}\)
\(dV = -3.1x^{2}dx\)
now integrate
\(\int_{x=0}^{x=7.5}dV = -\int_{0}^{7.5}3.1x^{2}dx\)
\(V(x=7.5m)-V(x=0 m ) = -\frac{3.1 (7.5^{3}- 0^{3})}{3} = -435.94\)
so
V = integral of E*dx = itnegral of 3.1 x^2 from 0 to 7.5 = 3.1
x^3/3 from 0 to 7.5 = 3.1*7.5^3/3=435.9 V
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