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Need clarity, kindly explain! - Electrostatics - JEE Main-4

An electric field \vec{E}=\left ( 25\: \hat{i}+30\: \hat{j} \right )NC^{-1}exists  in  a region of space. If the potential at the origin is taken to be zero then the potential at x=2 m, y=2 m is :

 

  • Option 1)

    -130 J

  • Option 2)

    -120 J

  • Option 3)

    -140 J

  • Option 4)

    -110 J

 
Answers (2)
106 Views
N neha
V Vakul

As we learnt in

In space -

E_{x}=\frac{-dv}{dx}  ,  E_{y}=\frac{-dv}{dy}    ,  E_{z}=\frac{-dv}{dz}

-

 

 dv=-\vec{E}.\vec{dr} \Rightarrow \int dV=-\int \vec{E}.\vec{dr}

\vec{dr}= dx\hat{i} + dy\hat{j} +dz\hat{k}

\vec{E}= (25\hat{i}+ 30\hat{j})Nc^{-1}

\int dV= -\int (25\hat{i}+ 30\hat{j}) (dx\hat{i} + dy\hat{j})

\int_{0}^{V} dV ={\int_{0}^{2} 25 dx +\int_{0}^{2}30 dy}

V-0= {{25[x]_{0}^{2} +30 [y]_{0}^{2}}}

V= -[25\times 2 + 30\times 2]\Rightarrow V=-110J/C

V= -110J/C


Option 1)

-130 J

Incorrect option

Option 2)

-120 J

Incorrect option

Option 3)

-140 J

Incorrect option

Option 4)

-110 J

Correct option

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