Derive electric field inside and outside of a atom having nuclear charge ze?
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Explanation:
ved!
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An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge, +Ze (the nucleus) at the center of a sphere of radius R with uniformly distributed negative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number electrons in the negative sphere.
Estimate the charged enclosed within a sphere with the nucleus at its center, and the radius of r, smaller than R.
Use Gauss' law to obtain the electric field inside this atom.
A uranium atom has Z = 92 and R = 0.10 nm. Estimate the electrostatic force that an electron would experience at r = R/2?
Assuming that the electron in c) is in the uniform circular motion around the nuclear, estimate the speed of the electron.
What is the electric field outside the atom? Explain your result.
The electric potential energy at a certain position is defined as the amount of work by the electric force, needed to bring a charge from the infinite to the position. Estimate the potential energy of the electron, considered in
c), at r = R/2 in the uranium atom.
Estimate the electric potential at r = R/2.
→p =
−→d
where −→d points from the negative to positive charge.
The concept of electric potential is especially useful for
calculating the electric field for the electric dipole.
The electric potential relative to infinity at the
point in a figure 1 is given by:
= 1
4
Ã
£
− ¡
2
¢
cos 2
¤ −
£
+ ¡
2
¢
cos 1
¤
!
where 2 is the angle for the positive charge and 1 for
the negative charge. Let then 1 ≈ 2 ≈ ,
and the equation simplifies to:
=
4
cos
h
2 − ¡
2
¢2
cos2
i '
4
cos
2
The electric dipole moment is given by:
−→p =bi
that is, the electric dipole moment is a vector quantity
as opposed to the monopole moment .
Thus the electric potential relative to infinity can
be written as:
=
−→p · br
42
since bi·br = cos where br point from the electric dipole
towards the point .