Electric potential due to a space is given by ϕx, y, z=ϕoxox, when xo=5 m and ϕo=8 V. Find the electric field at 10m, 5m, 5m

We have E=dVdx=−ddxϕ0x0x=−ϕ0x0×−1x2=40x2So, E/10,5,5=40102=0.4V/m

We have E=dVdx=−ddxϕ0x0x=−ϕ0x0×−1x2=40x2So, E/10,5,5=40102=0.4V/m

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Electric potential due to a space is given by $ϕ (x, y, z) = ϕ_{o} \frac{x_{o}}{x},$ when $x_{o} = 5 m$ and $ϕ_{o} = 8 V.$ Find the electric field at $(10m, 5m, 5m)$

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$- 4.0 {V m}^{- 1} \hat{i}$

$0.40 {V m}^{- 1} \hat{i}$

$4.0 {V m}^{- 1} \hat{i}$

$- 0.40 {V m}^{- 1} \hat{i}$

answer is A.

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We have $E = \frac{d V}{d x} = - \frac{d}{d x} [\frac{ϕ_{0} x_{0}}{x}] = - ϕ_{0} x_{0} \times - \frac{1}{x^{2}} = \frac{40}{x^{2}}$

So, $E / (10, 5, 5) = \frac{40}{10^{2}} = 0.4 V / m$

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