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  4. The electric potential V is given as a function of distance x (metre) by V=(5x2+10x-4)V. Value of electric field at x=1 m is:

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Q. The electric potential $V$ is given as a function of distance $ x $ (metre) by $ V=(5x^{2}+10x-4)V. $ Value of electric field at $ x=1\,m $ is:

Jharkhand CECEJharkhand CECE 2006

Solution:

$ E=-\frac{dV}{dx} $
Electric field $ E $ is given by
$ E=-\frac{dV}{dx} $
Given, $ V=5x^{2}+10x-4 $
$ \therefore E=\frac{dV}{dx}=10x+10 $
At $ x=1,E=-(10\,\,\times \,\,1\,+\,10)$
$=-20\,V/m $