In a region, the potential is represented by V(x,y,z) = 6x - 8xy - 8y + 6yz, where V is in volts and x, y, x are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is:

  • Option 1)

    6\sqrt{5} N

  • Option 2)

    30 N

  • Option 3)

    24 N

  • Option 4)

    4\sqrt 35 N

 

Answers (1)
D Divya Saini

 

In space -

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

-

 

 V \left ( x,y,z \right )=6x-8xy-8y+6yz

 

\vec{E} = - \vec{V}V = \frac{\vartheta\vec{V}}{\vartheta x}\hat{j}-\frac{\vartheta\vec{V}}{\vartheta y}\hat{j}-\frac{\vartheta\vec{V}}{\vartheta z}\hat{k}

\vec{E} = \left ( 6-8y \right )\hat{j} -\left ( -8x-8-6z \right )\hat{j}-\left ( 6y \right )\hat{k}

= -\left ( 6-8y \right )\hat{j}+\left ( 8x+8-6z \right )\hat{j} -6y\hat{k}

\vec{E} = 2\hat{j}+10\hat{j}-6 \;\hat{k}

\begin{vmatrix} \bar{E} \end{vmatrix}=\sqrt{2^{2}}+10^{2}+6^{2}=\sqrt{140}=2\sqrt{35}

q\begin{vmatrix} \bar{E} \end{vmatrix}= 4\sqrt{35} N


Option 1)

6\sqrt{5} N

Incorrect

Option 2)

30 N

Incorrect

Option 3)

24 N

Incorrect

Option 4)

4\sqrt 35 N

Correct

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