A uranium nucleus has 92 protons. (a) Determine the magnitude of the E⃗ field at a distance of 0

step 1 Okay, so we know the electric fuel is equal to kK over r square. K is K is K is K, K is a consta

A uranium nucleus has 92 protons. (a) Determine the...

A uranium nucleus has 92 protons. (a) Determine the magnitude of the $\vec{E}$ field at a distance of $0.58 \times 10^{-12} \mathrm{m}$ from the nucleus (about the radius of the innermost electron orbit around the nucleus). (b) What is the magnitude of the force exerted on an electron by this $\vec{E}$ field? (c) What assumptions did you make? If the assumptions are not valid, will the magnitude in part (b) be an overestimate or underestimate of the actual value?

A uranium nucleus has 92 protons. (a) Determine the magnitude of the $\vec{E}$ field at a distance of $0.58 \times 10^{-12} \mathrm{m}$ from the nucleus (about the radius of the innermost electron orbit
around the nucleus). (b) What is the magnitude of the force exerted on an electron by this $\vec{E}$ field? (c) What assumptions did you make? If the assumptions are not valid, will the magnitude in part (b) be an overestimate or underestimate of the actual value?

Key Concepts

Assumptions in Electrostatic Modeling

In many problems involving electric fields and forces, simplifying assumptions are made such as treating nuclei as point charges and electrons as test charges. These assumptions ignore complex effects like electron shielding, quantum mechanical effects, and relativistic corrections. Recognizing these assumptions is important because if they do not hold true, the calculated values might overestimate or underestimate the actual forces involved.

Force on a Charge in an Electric Field

The force experienced by a charge in an electric field is given by F = qE, where F is the force, q is the magnitude of the charge, and E is the electric field strength. This relationship directly connects the electric field to the mechanical force on a charged particle, allowing predictions and calculations of particle dynamics in electric fields.

Coulomb's Law

Coulomb's law describes the force between two point charges. It states that the magnitude of the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle is fundamental in calculating electric forces and underpins the determination of electric fields produced by point charges.

Electric Field of a Point Charge

The electric field created by a point charge is calculated using the formula E = kQ/r², where E is the electric field, k is Coulomb's constant, Q is the charge of the source, and r is the distance from the charge. This concept is crucial for determining the field strength at a certain distance, which is then used to compute the force experienced by other charges introduced into the field.

Transcript

00:01 Okay, so we know the electric fuel is equal to kk over r square.

00:04 K is k is k is k, k is a constant.

00:05 Q is the charge and the r is the distance.

00:08 We know kowloon constant is equal 9 times 10 to power 9 newton times meter square for kulang square.

00:13 And the distance is given as 0 .5a times 10 to the power of negative 12 meter, which is the radius of the nuclear.

00:22 And the charge on nuclear is 92e, since there are 92 protons there, which will give us the total charge on the nuclear system about 1 .472 times 10 to the power of negative 17 kulams.

00:36 So therefore, we can determine the electric field, which is equal to 9 times 10 to the power of 9, newton times medium square for koulon square, and n times 1 .472 times 10 to the power of negative 17 koulon, over 0 .58 times, oh, sorry, 10 to the power of a negative, negative 12 meter, and then to the power of 2.

01:20 And this will give us the electric fuse about 3 .938 times 10 to the power of 17 newton per cool.

01:41 And for question b was asking us the force that was exerted by the electron.

01:47 When a force can be equal to the charge of electron times the electrophue, which is negative e, since the electron has a negative charge.

01:54 So therefore we have force is equal to negative 1 .6 times 10 to the power of negative 19 cologne, and then times the electrophil, which is 3 .938 times 10 to the power of 17, newton per cologne.

02:14 And this will give us the electric force is about negative 0 .063 newton...

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