Question 757: Electrostatics & Capacitance

Question

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

Accepted Answer

$$\overrightarrow E  =  - \overrightarrow 
abla  V$$
where $$\overrightarrow 
abla   = \widehat i{\partial  \over {\partial x}} + \widehat j{\partial  \over {\partial y}} + {\partial  \over {\partial z}}$$
$$\overrightarrow E  =  - \left[ {\widehat i{{\partial V} \over {\partial x}} + \widehat j{{\partial V} \over {\partial y}} + \widehat k{{\partial V} \over {\partial z}}} ight]$$
Here, V = 4x
2
$$ 	herefore \overrightarrow E  =  - 8x\widehat i$$
The electric field at point (1, 0, 2) is
$${\overrightarrow E _{\left( {1,0,2} ight)}} =  - 8\widehat iV{m^{ - 1}}$$
So electric field is along the negative X-axis.

Answer

8 along negative X-axis

Answer

8 along positive X-axis

Answer

16 along negative X-axis

Answer

16 along positive X-axis

Electrostatics & Capacitance

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

Choose the correct answer: