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  • The electric potential in a certain region is expressed by <img alt="\mathrm{v=6 x-8 x y^2-8 y+6 y z-4 z^2 }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bv%3D6%20x-8%20x%2

The electric potential in a certain region is expressed by \mathrm{v=6 x-8 x y^2-8 y+6 y z-4 z^2 }  volts. The magnitude of a force acting on a charge of 2C situated at the origin will be -

Option: 1

2 N


Option: 2

6 N


Option: 3

8 N


Option: 4

20 N


Answers (1)

best_answer

Potential is given by -
\mathrm{\begin{gathered} v=6 x-8 x y^2-8 y+6 y z-4 z^2 \\ \vec{E}=-\frac{\partial v}{\partial x} \hat{\imath}-\frac{\partial v}{\partial y} \hat{j}-\frac{\partial v}{\partial z} \hat{k} \\ \vec{E}=-\left(6-6 y^2\right) \hat{i}-(-8 x \cdot 2 y-8+6 z) \hat{j}-(6 y-4 \cdot 2 z) \hat{k} \end{gathered} }

At origin (0,0,0) then -
\mathrm{\begin{aligned} & \vec{E}=-6 \hat{i}+8 \hat{j} \\ & |\vec{E}|=\sqrt{6^2+8^2}=\sqrt{100} \Rightarrow 10 \end{aligned} }

Force (F)= \mathrm{E \times q=10 \times 2=20 \mathrm{~N} } Ans

Posted by

Rakesh

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