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When we discuss the forces within an atom, Coulomb's law is a fundamental principle we rely on. This law describes how electrically charged particles attract or repel each other depending on their charges and the distance between them. It is mathematically expressed as:
\[E = \frac{kQ}{r^2}\]
In this equation, \(E\) represents the electric field strength, \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, N.m^2/C^2\)), \(Q\) is the charge of the particle, and \(r\) is the distance from the charge center to the point where the field is measured. In the context of an atom like uranium, Coulomb's law enables us to calculate the electric field just outside its nucleus by substituting the number of protons and the radius of the nucleus into this equation.

A uniformly charged shell is an idealized concept often used in physics to simplify the complex interactions in systems with spherical symmetry. In the case of atomic structures, it can be particularly helpful when we think of an electron cloud around a nucleus. The idea is to assume that the electrons form a shell with a charge density that is uniform—that is, the same at all points on the shell.
An intriguing property of a uniformly charged shell is that the electric field inside of it is zero. This occurs due to the principle of superposition, meaning the field created by each portion of the charged shell is exactly canceled out by fields from the rest of the shell when you're inside it. Therefore, at the nucleus of the atom, which lies within the shell, the electrons do not affect the nucleus with any electric field.

The concept of the electric field due to a point charge is crucial when studying atomic structure, especially for understanding how protons in the nucleus affect the surrounding space. A point charge refers to an idealized charge located at a single point in space. While actual charges have a volume, protons in a large nucleus can sometimes be approximated as point charges for simplicity.
The electric field produced by a point charge is radially outward if the charge is positive, and inward if the charge is negative. Its magnitude decreases with the square of the distance from the charge. This inverse-square relationship is captured by the Coulomb's law formula:\[E = \frac{kQ}{r^2}\]
Applying this concept to our uranium atom, we determine the electric field a specific distance from the nucleus (represented by \(r\)) by considering the nucleus as a point charge with a quantity equal to the number of protons multiplied by the elementary charge.

In atomic models, an electron cloud represents the area around the nucleus where there's a high probability of finding an electron. Unlike planets orbiting a sun, electrons do not have a fixed path around the nucleus but instead form a 'cloud' due to quantum mechanical effects.
Modeling electrons as a cloud with a uniform density allows us to apply the concept of a uniformly charged shell to predict the electric field inside the nucleus as a result of the electrons' presence. The net electric field at the nucleus due to this electron cloud, following the properties of a uniformly charged shell, is zero. This means the electric field from this shell does not exert a force on the protons in the nucleus, an essential concept when considering the internal workings of an atom.