Assume that an electric field E =30 x^2 i  exists in space. Then the potential difference

Q: Assume that an electric field $\displaystyle \vec{E} = 30 x^2 \hat{i} $ exists in space. Then the potential difference VA-V0 where V0 is the potential at origin and VA potential at x = 2 m is

(a) – 80 V

(b) 80 V

(c) 120 V

(d) -120 V

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Ans: (a)

Sol: $\displaystyle dV = -\vec{E}.\vec{dx} $

$\displaystyle dV = -30 x^2 \hat{i}.dx \hat{i} $

$\displaystyle dV = -30 x^2 dx $

$\displaystyle \int_{V_0}^{V_A} dV = -30 \int_{0}^{2} x^2 dx $

$\displaystyle V_A – V_0 = -[10 x^3]_{0}^{2} $

$\displaystyle V_A – V_0 = – 80 \; V $