# E&M question: suppose the speed of light is greater in an alternate universe?

1. Dec 18, 2008

### saraaaahhhhhh

This is not a question of 'how' to do a problem; I know the answer to it and would like an explanation of why this is the correct answer, if possible! Thanks in advance!

Suppose there exists another universe where the laws of electrostatics and special relativity and the relevant physical constants are the same with one exception: the speed of light is much greater than 3x10^8 m/s. Which of the following things are true?

a.)gravitational acceleration of objects would be faster in the other universe than ours
b.) electric field in between plates of a parallel plate capacitor would be weaker in the other universe than in our own
c.) electric field in between plates of a parallel plate capacitor would be stronger in the other universe than in our own
d.) magnetic field produced by a current carrying wire would be weaker in the other universe than in our own
e.) magnetic field produced by a current carrying wire would be stronger in the other universe than in our own

The listed answer is D, but I don't see why B wouldn't work as well?

Thanks again! :)

Last edited: Dec 18, 2008
2. Dec 19, 2008

### Avodyne

Well, I think it's a poorly worded question, since it's not completely clear what constants to hold fixed as the speed of light changes. In E&M, you could hold $\varepsilon_0$ fixed or $\mu_0$ fixed, but not both, because $\varepsilon_0\mu_0=1/c^2$. The question says that "the laws of electrostatics" are the same, and if we interpret that to mean that $\varepsilon_0$ is held fixed, then D is the right answer. But you could argue that the question is ambiguous, and that C is also possibly correct.

Edit: I originally said "B is also possibly correct", but actually it would be C, since if $c$ goes up with $\mu_0$ fixed, then $\varepsilon_0$ goes down, so the electric field produced by a point charge (which goes like $1/\varepsilon_0$) goes up.

Last edited: Dec 19, 2008
3. Dec 19, 2008

### turin

... or light is not an electromagnetic phenomenon in that univserse ...

... very poorly worded question.

4. Dec 19, 2008

### Redbelly98

Staff Emeritus
Well, if the laws of electrostatics are the same then doesn't it stand to reason that the electric field between capacitor plates would have to be the same? As would the electrostatic force between two charges:

$$F = \frac{1}{4 \pi \epsilon_o}\frac{q_1 \ q_2}{r^2}$$

So εo would have to be the same, no?

5. Dec 19, 2008

### saraaaahhhhhh

Yeah, I didn't realize it said the laws of electrostatics would be the same. I think the question is perfectly clear:) Thanks!

6. Dec 19, 2008

### Andrew Mason

It appears that the writer of the question assumes that this new universe would be exactly like our own except that the speed of light would be greater ie. that Maxwell's laws would be the same but the values for $\mu_0 \text{ and } \epsilon_0$ would each be smaller.

Therefore, Gauss' law would still apply:

$$\oint \vec{E}\cdot d\vec{A} = \frac{Q}{\epsilon_0}$$

as would Ampere's law:

$$\oint \vec{B}\cdot d\vec{s} = \mu_0 I$$

So, would the electric field would be stronger or weaker in the new universe for a given electric charge at a given position? Would the magnetic field associated with a given electric current be stronger or weaker at a given position?

What is the expression for the electric field, E, between two parallel plates of a charged capacitor? How would a lower value for $\epsilon_0$ affect E?

AM

Last edited: Dec 19, 2008
7. Dec 19, 2008

### Andrew Mason

If Gauss' law and Special Relativity remained unchanged and if $\epsilon_0$ remained unchanged, then $\mu_0$ would remain unchanged as well. Magnetism is simply the effect of special relativity on moving electric charges. A magnetic field is really the relativistic effect of a moving electric field. So the values of $\epsilon_0$ and $\mu_0$ would have to decrease proportionately if the speed of light increased keeping special relativity intact.

AM