Question

a. Suppose that $\overrightarrow{E}=\overrightarrow{0}V/m$throughout some region of space. Can you conclude that $V=0V$in this region? Explain.

b. Suppose that $V=0V$ throughout some region of space. Can you conclude that $\overrightarrow{E}=\overrightarrow{0}V/m$ in this region? Explain.

Short answer

(a) No, $v$is not necessarily $0$.

(b) Yes, $\overrightarrow{\left|E\right|}$is zero

Step-by-step solution

Given information and formula used  

Given :

a. $\overrightarrow{E}=\overrightarrow{0}V/m$

b. $V=0V$

Theory used :

In the region of constant electric potential, electric field is zero so there is no charge inside the region.

Electric field is the negative slope (“derivative” or “gradient”) of the potential.

$\overrightarrow{E}=-\frac{\Delta V}{\Delta x}$

Determining if  V = 0 Vin this region 

a) No.

However, you can deduce that $∆V=0V$, implying that the potential in that region of space is constant.

Determining if E→= 0→ V/m

(b) The answer is yes.

Because $\overrightarrow{E}=-\frac{\Delta V}{\Delta x}$, when $V$is constant in a region of space, $E=0V/m$.