Error for Electric Field Calculation

[bphysics]

Homework Statement

Need to calculate an electric field $$\left|E\right|$$. I'm calculating this off of a map of equi-potential lines and electric field lines which have been determined by semiconducting paper.

I then need to calculate the error -- this is where I am having trouble.

Homework Equations

$$\left|E\right| = \frac{\Delta V}{\Delta l}$$

$$\frac{\delta E}{E}\right)= \sqrt{\left(\frac{\delta V}{V}\right)^2 + \left(\frac{\delta l}{l}\right)^2}$$

The Attempt at a Solution

I'm not 100% sure I understand how to use this equation for error. Can anyone offer any assistance?

 

[anathema]

Calculating the error in the electric field can be a bit tricky, but I can definitely offer some assistance. The equation you have listed is correct, but it is important to understand what each term represents.

First, \left|E\right| represents the magnitude of the electric field, which is the strength of the electric field at a certain point. This can be calculated by taking the potential difference (\Delta V) and dividing it by the distance (\Delta l) between two equi-potential lines.

Next, the term \frac{\delta E}{E} represents the relative error in the electric field. This takes into account the uncertainties in both the potential difference and the distance. The equation for this is the square root of the sum of the squares of the relative errors in \Delta V and \Delta l.

To find the absolute error in the electric field, you can simply multiply the relative error by the magnitude of the electric field. So the final equation for the error in the electric field would be:

\delta E = \frac{\delta E}{E} \times \left|E\right|

I hope this helps clarify the equation for you. If you have any further questions, please don't hesitate to ask. Good luck with your calculations!