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Electrostatic Potential And Capacitance

Question
CBSEENPH12039494
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Assume that an electric field straight E equals space 30 space straight x squared space straight i with hat on top exists in space. Then the potential difference VA – VO, where VO is the potential at the origin and VA the potential at x = 2 m is:

  • 120 J

  • -120 J

  • -80 J

  • 80 J

Solution

C.

-80 J

As we know, potential difference VA -Vo is 
dV = - Edx
integral subscript straight V subscript straight o end subscript superscript straight V subscript straight A end superscript dV space equals negative integral subscript 0 superscript 2 30 space straight x squared dx straight V subscript straight A space minus straight V subscript straight O space equals space minus space 30 space straight x space open square brackets straight x cubed over 3 close square brackets squared space equals negative 10 space straight x left square bracket 2 cubed minus 0 cubed right square bracket space equals space minus 10 space straight x 8 space equals space minus 80 space straight J

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