Question

What is the potential difference $∆V_{34}$in Figure EX26.16?

Short answer

The potential difference is$\mathbf{20}\mathbf{}\mathit{V}$

Step-by-step solution

Given information and theory used   

Given :

Theory used :

To find the potential difference between two points :

Step 1: Determine the strength of the field, $E$, and the distance between the two points, $d$.

Step 2: Use the formula $\Delta V=Ed$to calculate the potential difference between the two points.

Calculating the potential difference 

We may express the potential at point 1 as

$$\begin{gathered} ∆V_{41}=-60=V_1-V_4 \\ \Rightarrow V_1=V_4-60 \end{gathered}$$

by knowing the potential difference between locations 4 and 1.

Again, we may express the potential at point 2 as

$$\begin{gathered} ∆V_{12}=30=V_2-V_1 \\ \Rightarrow V_2=V_1+30 \end{gathered}$$

by knowing the potential difference between locations 1 and 2.

By substituting this result in the previous one, we get

$V_2=V_4-60+30=V_4-30$

We may express the potential at point 3 as

$$\begin{gathered} ∆V_{23}=50=V_3-V_2 \\ \Rightarrow V_3=V_2+50 \end{gathered}$$

by knowing the potential difference between points 2 and 3.

We may calculate $V_3=V_4-30+50=V_4+20$by substituting our result for the potential at point 2 at the preceding one.

The possible difference between points 3 and 4 is now obvious:

$∆V_{34}=V_3-V_4=\boxed{\mathbf{20}\mathbf{}\mathit{V}}$.