# Voltage using different references

• darioslc
In summary: E}.Therefore, the field is not affected by the change in reference point. In summary, the conversation discusses the effect of changing the zero potential reference point on the electric potential and field of a solid sphere uniformly charged with Q and radii R. It is found that the potential changes by a constant amount, but the electric field remains the same regardless of the reference point. This is compared to the gravitational equivalent and is a universal phenomenon.
darioslc
Homework Statement
How the choice of zero voltage at the origin changes the electric field.
Relevant Equations
##\oint_S\vec{E}\cdot d\vec{S}=\frac{Q}{\varepsilon_0}##
##V(r)=-\int \vec{E}\cdot d\vec{l}##
The problem is for a solid sphere uniformly charged with Q and radii R.
First I calculated taked ##V(\infty)=0##, giving me for :
\begin{align*} V(r)=&\frac{3Q}{8\pi\varepsilon_0 R}-\frac{Q}{8\pi\varepsilon_0 R^3}r^2\qquad\text{if r<R}\\ V(r)=&\frac{Q}{4\pi\varepsilon_0 r}\quad\text{if r\geq R}\\ \end{align*}
so far well, but when I calculated the voltage with ##V(0)=0## I get a little similar expression:
\begin{align*} V(r)=& \begin{cases} -\frac{Q}{8\pi\varepsilon_0 R^3}r^2\qquad\text{if r<R}\\ -\frac{3Q}{8\pi\varepsilon_0 R}+\frac{Q}{4\pi\varepsilon_0 r}\qquad\text{if r\geq R}\\ \end{cases} \end{align*}
for both, I used the expression of the electric field
\begin{align*} \vec{E}(r)=& \begin{cases} \frac{Q}{4\pi\varepsilon_0R^3}r^2\qquad\text{if r<R}\\ \frac{Q}{4\pi\varepsilon_0r}\qquad\text{if r\geq R}\\ \end{cases} \end{align*}

In both cases, when I apply the gradient ##\vec{E}=-\nabla V## I get the same field, and I can't understand how can change the field if I take other zero-point references, is not independent of potential? ie, always I get the same field
Maybe have an error in calculus, but I didn't found it.

Thanks a lot!

I believe potential is always measured relative to something, whereas the electric field is 'absolute'/fixed. Therefore, when you set the zero potential point to a different place, you can get a different potential as you are measuring relative to a different point. An electric circuit is an example; when we say the voltage is '5 V', we really mean that it has a potential that is +5V greater than the chosen zero (i.e. ground). If we chose the ground elsewhere, then the potential would be different I think.

DaveE
darioslc said:
In both cases, when I apply the gradient ##\vec{E}=-\nabla V## I get the same field

Hi. You are supposed to get the same field. Changing the zero potential reference point does not affect the field.

Changing the reference point simply adds a constant amount to every point's potential.

A change from 100V to 150V over a some distance gives the same field as a change from 120V to 170V over the same distance.

Think of the equivalent gravitational situation: g = -9.81m/s² at the Earth's surface whether you choose to take V=0 at ground level or V=0 at ∞.

Hi, thanks for your responses. Then the field shouldn't vary? this is what I was thinking, or the question is a little captious.

That's right - the field cannot be changed by changing the reference point. Note that this in not limited to spherical charge distributions, it is always true. I guess the question was set to make you think about why it is true.

If we change the zero reference point, the potential at every point changes by the same fixed amount (say k). Since constants disappear on differentiation:
$$\vec{E}=-\nabla (V+k) = -\nabla (V)$$

## 1. What is voltage?

Voltage is a measure of the electric potential difference between two points in a circuit. It is the force that pushes electrons through a conductor, creating an electric current.

## 2. How is voltage measured?

Voltage is measured using a voltmeter, which is connected in parallel to the circuit. It is typically measured in volts (V) using a multimeter or other measuring device.

## 3. What is a reference voltage?

A reference voltage is a known, fixed voltage that is used as a point of comparison for other voltages in a circuit. It is often used as a standard for measuring and calibrating other voltages.

## 4. How does using different reference voltages affect voltage measurements?

Using different reference voltages can affect voltage measurements in a few ways. It can impact the accuracy and precision of the measurement, and it can also introduce errors or discrepancies in the measurement if the reference voltage is not stable or consistent.

## 5. Why might someone use different reference voltages?

Someone might use different reference voltages for a variety of reasons. For example, they may need to measure a specific range of voltages that requires a different reference voltage, or they may want to compare the voltage readings from different circuits that use different reference voltages. Additionally, different types of circuits or components may require different reference voltages for accurate measurements.

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