The electric charge of a proton is distributed over a volume. The distribution o

Question

The electric charge of a proton is distributed over a volume. The distribution of the proton can be approximated by the exponential equation rho = e/(8*pi*b)exp(-r/b). r is the radial position inside the proton and b equals .23 * 10^-15 m. Find the electric field as a function of the radial distance. What is the magnitude of the electric field at r = 1 * 10^-15 m? Compare the electric field strength you find to that of a point charge of magnitude e. At what distances r do these two differ by 10% or more? Hint: You will need to integrate over the volume of a sphere where the volume element is dV = r^2*dr d(cos(theta))d(phi). Since the charge distribution only depends on r the integrals over the angles  and  are simple and give a factor of 4*pi times the radial integral. I'm confused as to how to even approach this problem. Any and all help would be much appreciated. Thanks in advance

Explanation / Answer

The Stefan-Boltzmann law (S-B) describes the total emission from a flat surface that is equally radiated in all directions, (is isotropic/hemispherical). Stefan found this via experimental measurement, and later his student Boltzmann derived it mathematically. 2) The validity of equally distributed hemispherical EMR is demonstrated quite well by observing the Sun. (with eye protection). It appears to be a flat disc of uniform brightness, but of course it is a sphere, and at its outer edge, the radiation towards Earth is tangential from its apparent surface, not vertical. It is not a perfect demonstration because of a phenomenon called limb darkening, due to the Sun not having a definable surface, but actually plasma with opacity effects. However, it is generally not apparent to the eye and the normally observed (shielded) eyeball observation is arguably adequate for purpose here.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.