Verified Solution • 2025–26 Session moderate

QJEEM14Ph4d7c: JEE Main 2014 Physics - Class 12 JEEM14Ph4d7c Solution: Assume that an electric field exists in space. Then the…

Assume that an electric field E→=30x2i^\overrightarrow E = 30{x^2}\widehat i exists in space. Then the potential difference VA−VO,{V_A} - {V_O}, where VO{V_O} is the potential at the origin and VA{V_A} the potential at x=2x=2 mm is :

Multiple Choice Options

  • A 120120 J/CJ/C
  • B −120-120 J/CJ/C
  • C −80-80 J/CJ/C
  • D 8080 J/CJ/C

Step-by-Step Verified Solution

Potential difference between any two points in an electric field is given by,

dV=−E→.dx→dV = - \overrightarrow E .\overrightarrow {dx}

∫VOVAdV=−∫0230x2dx\int\limits_{{V_O}}^{{V_A}} {dV = - \int\limits_0^2 {30{x^2}} } dx

VA−VO=[10x3]02=−80J/C{V_A} - {V_O} = \left[ {10{x^3}} \right]_{0}^2 = - 80J/C

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