Question 763: Electrostatics & Capacitance

Question

The electric potential at a point (x, y, z) is given by V = $$-$$x
2
y $$-$$ xz
3
+ 4
The electric field at that point is

Accepted Answer

The electric potential at a point,
V = Ã¢ÂÂx
2
y Ã¢ÂÂ xz
3
+ 4.
The field
$$\overrightarrow E  =  - \overrightarrow 
abla  V =  - \left( {{{\partial V} \over {\partial x}}\widehat i + {{\partial V} \over {\partial y}}\widehat j + {{\partial V} \over {\partial z}}\widehat k} ight)$$
$$ 	herefore \overrightarrow E  = \widehat i\left( {2xy + {z^3}} ight) + \widehat j{x^2} + \widehat k\left( {3x{z^2}} ight)$$

Answer

$$\overrightarrow E  = \widehat i2xy + \widehat j\left( {{x^2} + {y^2}} \right) + \widehat k\left( {3xz - {y^2}} \right)$$

Answer

$$\overrightarrow E  = \widehat i{z^3} + \widehat jxyz + \widehat k{z^2}$$

Answer

$$\overrightarrow E  = \widehat i\left( {2xy - {z^3}} \right) + \widehat jx{y^2} + \widehat k3{z^2}x$$

Answer

$$\overrightarrow E  = \widehat i\left( {2xy + {z^3}} \right) + \widehat j{x^2} + \widehat k3x{z^2}$$

Electrostatics & Capacitance

The electric potential at a point (x, y, z) is given by V = $-x 2 y -$ xz 3 + 4 The electric field at that point is

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