Question

The electric potential v at any point $(x,y,z)$, all in meters in space is given by $V=4x^{2}V$. The electric field at the point $(1,0,2)$ in volt/meter, is:

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

Answer 1

The correct option is A

8 along negative X-axis

Step 1: Given Data

Electric potential $V=4x^2$

Step 2: Deriving

Formula: $\overrightarrow{E}=-(\hat{i}\frac{\partial V}{\partial x}+\hat{j}\frac{\partial V}{\partial y}+\hat{k}\frac{\partial V}{\partial z})$

⇒ $\overrightarrow{E}=-\hat{i}\left(8x\right)$

⇒ $E=-8x\hat{i}$

Step 3: Calculation

The given point is $(1,0,2)$

⇒ $E=-8\left(1\right)\hat{i}$

⇒ The electric field at that point is $8V/m$ along negative x-axis

Hence, the correct answer is option A