Electrostatics

JEE Main level, single correct, medium

188 of 311

Question 188 of 311

If the electric potential at any point (x,y,z)m\left(x,y,z\right)m in space is given by V=3x2V=3{x}^{2} volt. The electric field at the point (1,0,3)m\left(1,0,3\right)m will be :

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Answer: (C) 6Vm−16{Vm}^{-1}, directed along negative xx-axis.

Electric potential V=3x2V=3{x}^{2}
Electric potential and electric field are related as E=−dVdx=−6xE=-\dfrac{dV}{dx}=-6x.
At the point (1,0,3)m\left(1,0,3\right)m,
⇒E=−6×1=−6Vm−1\Rightarrow E=-6\times 1=-6V{m}^{-1}
Thus, electric field is 6Vm−16V{m}^{-1} along negative x‐x‐ axis.

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