Question

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

• A. 8 along negative X- axis
• B. 8 along positive X - axis
• C. 16 along negative X - axis
• D. 16 along positive Z - axis
  

Answer 1

The correct option is A 8 along negative X- axis

The electric potential V (x,y,z) = $4x^2$ volt
Now $\overrightarrow{E}=-(\hat{i}\frac{\partial V}{\partial x}+\hat{j}\frac{\partial V}{\partial y}+\hat{k}\frac{\partial V}{\partial z})$
Now $\frac{\partial V}{\partial x}=8x,\frac{\partial V}{\partial y}=0$ and $\frac{\partial V}{\partial z}=0,$
Hence $\overrightarrow{E},=-8x\hat{i}$ so at point (1m, 0, 2m)
$\overrightarrow{E}=-8\hat{i}$ volt/metre or 8 along negative X-axis