Assume that an electric field E→=30x2i^, exists in space. Then the potential difference VA – V0, where V0 is the potential at the origin and VA the potential at x = 2m is

Potential difference between two pointsVA−VB=∫AB E→⋅dr→,VA−V0=∫x=2x−0 30x2dx=10x320=−80V

Assume that an electric field E→=30x2i^, exists in space. Then the potential difference VA – V0, where V0 is the potential at the origin and VA the potential at x = 2m is

Potential difference between two pointsVA−VB=∫AB E→⋅dr→,VA−V0=∫x=2x−0 30x2dx=10x320=−80V

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

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120 V

-80 V

80 V

-120 V

answer is A.

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Detailed Solution

Potential difference between two points
$V_{A} - V_{B} = \int_{A}^{B} \vec{E} \cdot d \vec{r}, V_{A} - V_{0} = \int_{x = 2}^{x - 0} 30 x^{2} dx = {[10 x^{3}]}_{2}^{0} = - 80 V$

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Assume that an electric field E→=30x2i^, exists in space. Then the potential difference VA – V0, where V0 is the potential at the origin and VA the potential at x = 2m is

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