Question

The electric potential V at any point (x,y,z) all in meters in space is given by V=4x² volt .The electric field at the point (1,0,2) in V/m is:

8 along -ve X axis

8 along +ve X axis

16 along -ve X axis

16 along +ve X axis

Answer 1

$$\begin{gathered} \overrightarrow{E}=-\left(\frac{dV}{dx}\hat{i}+\frac{dV}{dy}\hat{j}+\frac{dV}{dx}\hat{k}\right) \\ GiventhatV=4x^2 \\ Here,\frac{dV}{dx}=8x;\frac{dV}{dy}=0;\frac{dV}{dz}=0 \\ \overrightarrow{E}=-8x \end{gathered}$$

Electric field at the point (1,0,2) is 8 along -ve X-axis