Question 928: Electrostats & Capacitance

Question

If potential (in volts) in a region is expressed as V(x, y, z) = 6xy $$-$$ y + 2yz, the electric field (in N/C) at point (1, 1, 0) is

Accepted Answer

Potential in a region V = 6xy Ã¢ÂÂ y + 2yz
As we know the relation between electric
potential and electric field is $$\overrightarrow E  = {{ - dV} \over {dx}}$$
$$\overrightarrow E  = \left( {{{\partial V} \over {\partial x}}\widehat i + {{\partial V} \over {\partial y}}\widehat j + {{\partial V} \over {\partial z}}\widehat k} \right)$$
$$\overrightarrow E  = \left[ {\left( {6y\widehat i + \left( {6x - 1 + 2z} \right)\widehat j + \left( {2y} \right)\widehat k} \right)} \right]$$
$${\overrightarrow E _{\left( {1,1,0} \right)}} =  - \left( {6\widehat i + 5\widehat j + 2\widehat k} \right)$$

Answer

$$ - \left( {2\widehat i + 3\widehat j + \widehat k} \right)$$

Answer

$$ - \left( {6\widehat i + 9\widehat j + \widehat k} \right)$$

Answer

$$ - \left( {3\widehat i + 5\widehat j + 3\widehat k} \right)$$

Answer

$$ - \left( {6\widehat i + 5\widehat j + 2\widehat k} \right)$$

Electrostats & Capacitance

If potential (in volts) in a region is expressed as V(x, y, z) = 6xy $-$ y + 2yz, the electric field (in N/C) at point (1, 1, 0) is

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