A hydrogen atom is made up of a proton of charge +Q = −1.60×10-19 C and an electron of charge −Q = −1.60×10−19 C. The proton may be regarded as a point charge at r = 0, the center of the atom. The motion of the electron causes its charge to be "smeared out" into a spherical distribution around the proton (Figure 1), so that the electron is equivalent to a charge per unit volume of ρ(r)=−(Q/πa03)e−2r/a0, where a0 = 5.29×10-11m is called the Bohr radius. (a) Find the total amount of the hydrogen atom's charge that is enclosed within a sphere with radius r centered on the proton. (b) Find the electric field (magnitude and direction) caused by the charge of the hydrogen atom as a function of r. c) Make a graph as a function of r of the ratio of the electric-field magnitude E to the magnitude of the field due to the proton alone.
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