# Magnetic Dipole Moment of an Electron

• jm321710
In summary, the conversation discusses how to calculate the magnetic dipole moment of a single atom, based on a given model. It also considers how the individual atomic magnetic dipoles of magnetic materials are aligned and how to calculate the net magnetic dipole moment of a piece of such material. The conversation also touches on the torque experienced by the material in a magnetic field. The suggested solution involves reviewing the relevant physics and considering the force keeping the electron in orbit and its angular momentum.
jm321710

## Homework Statement

I am so stuck on this, and would be very thankful for any help!

a). Calculate the magnetic dipole moment of a single atom, based on the following model: One electron travels at speed 7.40 × 10^6 m/s in a circular orbit of diameter 2 × 10^-10 m.
b). The individual atomic magnetic dipoles of magnetic materials (such as iron) are preferentially lined up to point in the same direction. If a fraction f of the dipoles are so aligned along the long axis (with the rest oriented randomly so that their magnetic dipole moments add vectorially to zero), what is the net magnetic dipole moment of a piece of such material (as shown in the diagram below); where w = 5.15 cm, h = 7.15 cm, l = 10.0 cm, and f = 0.40? Note, the material may be viewed as an array of cubes, each of which contains one atom, with only the outermost electron being considered, and is 2 × 10^-10 m on a side. Also assume the same speed for electron as in part a.)

c).What is the torque experienced by the piece of material in a field of 4.30 × 10-3 T, when the magnetic field is directed at right angles to the long axis of the material, as shown in the diagram?

M=NIA
i = Q/t
v= Δx/Δt

## The Attempt at a Solution

For part a). Area of the electron: A = π(1x10^-10)^2 = 3.4 x 10^-20
N = (7.4x10^6)/(2x10^-10) = 3.7 x 10^16
t = Δx/v => (2x10^-10)/(7.4x10^6) = 2.7 x 10 ^-17
i = (-1.6x10^-19)/(2.7 x 10 ^-17) =-0.005962
M = (3.7 x 10^16)(-0.005962)(3.4 x 10^-20)

The right answer should be 5.93 x 10 ^ -23, but I am doing something very wrong. I would be so thankful for any help.

First off, your allegedly right answer can't be right because it has no units.

That aside, I think you should go back and review the physics of what is going on in the problem. I'm not trying to be rude, but you clearly don't understand what the problem is about; your relevant equations aren't relevant at all.

Here is a hint: the electron is in an orbit. Some force must be keeping it in orbit. The fact that the problem is about magnetic moments might suggest what force. Also, things in orbit have angular momentum.

## What is the magnetic dipole moment of an electron?

The magnetic dipole moment of an electron is a measure of the strength and orientation of the electron's magnetic field, caused by its spin and orbital motion. It is usually represented by the symbol μ and has a magnitude of approximately 9.284x10^-24 joule per tesla.

## What causes an electron to have a magnetic dipole moment?

The magnetic dipole moment of an electron is caused by two factors: its spin and its orbital motion around the nucleus. The spin of an electron creates a small magnetic field, and when combined with its orbital motion, results in a net dipole moment.

## How is the magnetic dipole moment of an electron measured?

The magnetic dipole moment of an electron can be measured using a technique called electron paramagnetic resonance (EPR) spectroscopy. This involves placing the electron in a magnetic field and measuring the energy changes as the electron's spin flips between two quantum states.

## What is the significance of the magnetic dipole moment of an electron?

The magnetic dipole moment of an electron plays a crucial role in many physical phenomena, including the behavior of atoms and molecules in magnetic fields, the interactions between particles in particle accelerators, and the properties of materials in magnetic fields.

## Can the magnetic dipole moment of an electron change?

Yes, the magnetic dipole moment of an electron can change in certain circumstances, such as when the electron is in an external magnetic field or when it is interacting with other particles. However, the intrinsic value of the magnetic dipole moment of an electron remains constant.

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