# E.Field - E.Potential conversion

1. Oct 4, 2011

### Apteronotus

Hi,

I'm given a sensitivity threshold for a system in terms of the electric field. Is there any way of finding what the threshold is in terms of electric potential?
I know the relation $E=-\nabla\Phi$, but I dont see how I can apply it here.

ex.
Given $E_{t} \mbox{ in } [\frac{V}{m}]$ what is $\Phi_{t} \mbox{ in } [V]$?

2. Oct 4, 2011

### Born2bwire

That all depends on how the electric field behaves. If the electric field is a constant field, like in an idealized parallel plate capacitor, then the potential drop between two points along the field would be -E*d. But of course this only works out for a small set of idealized cases. If you were to look at say the voltage drop across the terminals of a connector (say a coaxial termination) then the voltage to electric field relationship would be much more complicated.

EDIT: I should also mention that the voltage may not indicate the peak electric field either. Take for example the case where the electric field is a sine function. The function is zero at the terminals and has a wavelength equal to the distance between the terminals. So in this case, the voltage difference between the terminals is zero (the integral of the electric field between the two points) yet the peak amplitude of the electric field can be anything.

Last edited: Oct 4, 2011
3. Oct 4, 2011

### Apteronotus

I have to admit that most of what you said is well beyond my knowledge.

The field is in fact oscillating and I'm given the frequency $f$. Hence, the information that I have is as follows:
My sensors can detect an electric field of peak amplitude $E_t$, when the frequency of the field is $f$.
Is there an easy way (for a non-physicist) to calculate the equivalent detection threshold for the electric potential?

4. Oct 4, 2011

### Apteronotus

Can anyone shed some light on this?

5. Oct 5, 2011

### Apteronotus

Before this post gets lost at the bottom of the list I was hoping someone could help me understand this a bit better.

6. Oct 5, 2011

### Born2bwire

Having only been given this information, no. We would need to know more about the sensor, how it works, about the incident radiation, and where you wish to measure the potential difference. We could probably make some simple approximations but we wouldn't know if they are applicable.