 Electrostatic potential
Question

# In a region, the potential is represented by V(x, y, z) = 6x - 8x - 8y + 6yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is

Moderate
Solution

## ${E}_{x}=-\frac{\partial V}{\partial x}=-\frac{\partial }{\partial x}\left(6x-8xy-8y+6yz\right)$${E}_{y}=-\frac{\partial V}{\partial y}=-\frac{\partial }{\partial y}\left(6x-8xy-8y+6yz\right)$${E}_{z}=-\frac{\partial V}{\partial z}=-\frac{\partial }{\partial z}\left(6x-8xy-8y+6yz\right)=-6y$$=\left(-6+8y\right)\stackrel{^}{i}+\left(8x+8-6z\right)\stackrel{^}{j}-6y\stackrel{^}{k}$At point (1, 1, 1)$\stackrel{\to }{E}=\left(-6+8\right)\stackrel{^}{i}+\left(8+8-6\right)\stackrel{^}{j}-6\stackrel{^}{k}$$=2\stackrel{^}{i}+10\stackrel{^}{j}-6\stackrel{^}{k}$$|\stackrel{\to }{E}|=\sqrt{{E}_{x}^{2}+{E}_{y}^{2}+{E}_{z}^{2}}=\sqrt{\left(2{\right)}^{2}+\left(10{\right)}^{2}+\left(-6{\right)}^{2}}$Electric force experience by the charge

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