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JamalS
JamalS
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Gauss' Law in crude terms reads that the Elec.electric field strength is proportional to the charge enclosed. In In integral form, it reads:

$$ \epsilon_0\int\vec{E}.\vec{dA} = Q $$$$ \epsilon_0\int\vec{E} \cdot \vec{dA} = Q $$

herewhere the dA$dA$ term is proportional to r^2$r^2$, for most cases. And alsoAlso, the E$\vec{E}$ term is proportional to an inverse square - So,so they conveniently cancel each other and we are left with constants that depend only on shape of the surface/region. If it were not the case, the evaluation of the integral is required, and we would have to use Coulomb's Law for the evaluation.

You can also have a look at the wiki page for Gauss Law, esp. this and the diveregence theorem for more clarity on the importance of the inverse square relation.

How would it have been, if this were false - well, that would require a redefinition of physics, and probably won't be allowed by this, in this Universe.

Gauss' Law in crude terms reads that the Elec. field strength is proportional to the charge enclosed. In integral form, it reads:

$$ \epsilon_0\int\vec{E}.\vec{dA} = Q $$

here the dA term is proportional to r^2, for most cases. And also, the E term is proportional to inverse square - So, they conveniently cancel each other and we are left with constants that depend only on shape of the surface/region. If it were not the case, the evaluation of the integral is required, and we would have to use Coulomb's Law for the evaluation.

You can also have a look at the wiki page for Gauss Law, esp. this and the diveregence theorem for more clarity on the importance of the inverse square relation.

How would it have been, if this were false - well, that would require a redefinition of physics, and probably won't be allowed by this, in this Universe.

Gauss' Law in crude terms reads that the electric field strength is proportional to the charge enclosed. In integral form, it reads:

$$ \epsilon_0\int\vec{E} \cdot \vec{dA} = Q $$

where the $dA$ term is proportional to $r^2$, for most cases. Also, the $\vec{E}$ term is proportional to an inverse square so they conveniently cancel each other and we are left with constants that depend only on shape of the surface/region. If it were not the case, the evaluation of the integral is required, and we would have to use Coulomb's Law for the evaluation.

You can also have a look at the wiki page for Gauss Law, esp. this and the diveregence theorem for more clarity on the importance of the inverse square relation.

How would it have been, if this were false - well, that would require a redefinition of physics, and probably won't be allowed by this, in this Universe.

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tpb261
tpb261
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Gauss' Law in crude terms reads that the Elec. field strength is proportional to the charge enclosed. In integral form, it reads:

$$ \epsilon_0\int\vec{E}.\vec{dA} = Q $$

here the dA term is proportional to r^2, for most cases. And also, the E term is proportional to inverse square - So, they conveniently cancel each other and we are left with constants that depend only on shape of the surface/region. If it were not the case, the evaluation of the integral is required, and we would have to use Coulomb's Law for the evaluation.

You can also have a look at the wiki page for Gauss Law, esp. this and the diveregence theorem for more clarity on the importance of the inverse square relation.

How would it have been, if this were false - well, that would require a redefinition of physics, and probably won't be allowed by this, in this Universe.