The electric field in a region is given by \overset{\rightarrow}{E} = \left(\right. Ax + b \left.\right) \hat{i}, where E is in NC–1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V1 and that at x = –5 is V2 then V1

Engineering

Physics

Electric Potential Energy and Electric Potential

Question

The electric field in a region is given by $\vec{E} = (Ax + b) \hat{i}$ , where E is in NC^–1 and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V₁ and that at x = –5 is V₂ then V₁ – V₂ is

180 V

320 V

–520 V

–48 V

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$\vec{E} = (20 X + 10) \hat{I}$

$V_{1} - V_{2} = - \int_{- 5}^{1} (20 x + 10) dx$

V₁ – V₂ = –(10x² + 10x)¹_–5

V₁ – V₂ = 10(25 – 5 – 1 – 1)

V₁ – V₂ = 180 V