The nuclei of large atoms, such as uranium, with 92 protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately 7.4×10−15 m. (a) What is the electric field this nucleus produces just outside its surface?

Verified step by step guidance

1. Identify the charge of the uranium nucleus. Since uranium has 92 protons and each proton has a charge of approximately $1.6 \times 10^{-19}$ Coulombs, the total charge $Q$ can be calculated as $Q = 92 \times 1.6 \times 10^{-19}$ Coulombs.
2. Use the formula for the electric field produced by a point charge at a distance $r$ from the charge. The formula is $E = \frac{kQ}{r^2}$, where $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N m}^2/\text{C}^2$).
3. Substitute the radius of the uranium nucleus for $r$ in the formula. Since the radius is given as $7.4 \times 10^{-15}$ meters, plug this value into the formula.
4. Calculate the electric field just outside the surface of the nucleus by substituting the values of $Q$, $k$, and $r$ into the electric field formula.
5. Interpret the result, understanding that the electric field value represents the intensity of the electric field at a point just outside the surface of the uranium nucleus.

Key Concepts

Electric Field

The electric field is a vector field that represents the force exerted by an electric charge on other charges in its vicinity. It is defined as the force per unit charge experienced by a positive test charge placed in the field. The electric field due to a point charge can be calculated using Coulomb's law, which states that the field decreases with the square of the distance from the charge.

Gauss's Law

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface. It states that the total electric flux is proportional to the enclosed charge, allowing for the calculation of electric fields in symmetric charge distributions. For a spherical charge distribution, this law simplifies the calculation of the electric field outside the sphere, as it can be treated as if all the charge were concentrated at its center.

Coulomb's Law

Coulomb's Law describes the electrostatic interaction between charged particles. It states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This law is fundamental in understanding how charges interact and is essential for calculating the electric field produced by charged objects, such as the nucleus of an atom.