Question

The electric potential V at any point O (x, y, z all in metres) in space is given by V = 4x² volt. The electric field at the point (1 m, 0, 2 m) in volt/metre is what ?

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Answer 1

Answer:

8 V/m

Step-by-step explanation:

Given :

V = 4x²

To find :

The electric field at the point (1 m, 0, 2 m)

Solution :

We know that,

$\boxed{\mathrm{E = \dfrac{dV}{dx}}}$

Differentiating potential with respect to x

$\implies \mathrm{\dfrac{dV}{dx} = \dfrac{d}{dx}(4x^{2})}$

We know that,

$\boxed{\mathrm{\dfrac{d}{dx}x^n = nx^{n-1}}}$

Thus,

$\implies \mathrm{\dfrac{dV}{dx} = 8x}$

As there is only x-variable in the equation, we need to find $\mathrm{E_{x=1}}$

So,

$\implies \mathrm{E_{x=1} = \dfrac{dV}{dx}_{x=1} = 8(1) = 8 \ V/m}$

$\therefore \underline{\boxed{\mathbf{E = 8 \ V/m}}}$

Hope it helps!!

Answer 2

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