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  • Electric potential at any point is <img alt="\mathrm{v=-5 x+3 y+\sqrt{15} z}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bv%3D-5%20x&plus;3%20y&plus;%5Csqrt%7B15%7D%20z

Electric potential at any point is \mathrm{v=-5 x+3 y+\sqrt{15} z} , then the magnitude of the electric field is -

Option: 1

3\sqrt{2}


Option: 2

4\sqrt{2}


Option: 3

5\sqrt{2}


Option: 4

7


Answers (1)

best_answer

\mathrm{\text { Potential }(V) =-5 x+3 y+\sqrt{15} z }
\mathrm{\text { Electric field }(E) =-\frac{d v}{d r} }
                                     \mathrm{ =-\frac{d}{d r}\left[\frac{d}{d x}(-5 x) \cdot \hat{\imath}+\frac{d}{d y} 3 y \hat{\jmath}+\frac{d}{d z} \sqrt{15 }z\right] }
                                      \mathrm{ =-\frac{d}{d r}[-5 \hat{i}+3 \hat{\jmath}+\sqrt{15} \hat{k}]}

Magnitude of electric field-
\mathrm{ |E|=\sqrt{(-5)^{2}+(3)^{2}+(\sqrt{15})^{2}} }
\mathrm{ |E|=\sqrt{25+9+15} }
\mathrm{|E|=\sqrt{49}=7 }  Ans.

Posted by

Suraj Bhandari

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