Question

What is the potential difference between $y_i=-5cm$ and $y_f=5cm$ in the uniform electric field $\overrightarrow{E}=(120,000\hat{i}-50,000\hat{j})V/m$?

Short answer

The potential difference is$\mathbf{5}\mathbf{}\mathit{k}\mathit{V}$

Step-by-step solution

Given information and formula used

Given :

$y_i=-5cm$ ; and $y_f=5cm$

Uniform electric field : $\overrightarrow{E}=(120,000\hat{i}-50,000\hat{j})V/m$

Formula used :

$∆V=-∆y·E_y$

Calculating the required the potential difference

We'll assume the $x$-component of the position is the same for both positions because we don't know anything about it; for example, both positions are measured along the $y$-axis.

$∆y=0.05-(-0.05)=0.1m$will be the difference in the $y$-component.

With this knowledge, the potential difference will be :

$$\begin{gathered} ∆V=-∆y·E_y=-0.1(-50000) \\ =\boxed{\mathbf{5000}\mathbf{}\mathit{V}} \end{gathered}$$