Q

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

An electric field 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

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As we learnt in

In space -

$\dpi{100} E_{x}=\frac{-dv}{dx}$  ,  $\dpi{100} E_{y}=\frac{-dv}{dy}$    ,  $\dpi{100} E_{z}=\frac{-dv}{dz}$

-

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

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

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

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

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

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

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