Assume that an electric field exists in space. Then the potential difference VA – VO, where V0 is the potential at the origin and VA the potential at x = 2 m is

Engineering

Physics

Electric Potential Energy and Electric Potential

Question

Assume that an electric field $\vec{E} = 30 x^{2} \hat{i}$ exists in space. Then the potential difference V_A – V_O, where V₀ is the potential at the origin and V_A the potential at x = 2 m is

120 J

–120 J

80 J

–80 J

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$E = - \frac{dU}{dx} = 30 x^{2}$

$DU = \int dU = - 30 \int_{0}^{2} x^{2} dx = - 10 [8 - 0]$

= – 80 J