**Finding the Magnetic Dipole Moment \( \vec{\mu} \) of the Current Loop**Consider the problem statement:Find the magnetic dipole moment \( \vec{\mu} \) of the current loop given in the figure.**Options:**A) \( I a^2 (-\hat{i} - \hat{j} + \hat{k}) \) B) \( I a^2 \left( \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \) C) \( I a^2 \left( -\hat{i} - \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \) D) \( I a^2 (-\hat{k}) \) E) \( I a^2 (-\hat{j}) \) **Explanation of the Diagram:**The diagram shows a 3D representation of a rectangular loop oriented in the x-y-z coordinate system with a current \( I \) flowing through it. - The loop is aligned with the coordinate planes such that: - One surface is parallel to the xz-plane. - Another surface is parallel to the yz-plane. - The loop creates a rectangular circuit and the dimensions of the rectangle are given as 'a' for both length and width.Arrows indicate the direction of the current steadily flowing through the loop:- \(\hat{x}\): The positive x-direction arrow indicates the current flowing parallel to the x-axis.- \(\hat{y}\): The positive y-direction arrow indicates the current is flowing parallel to the y-axis.- \(\hat{z}\): The current is flowing parallel to the z-axis.Use the right-hand rule: Point the thumb of your right hand in the direction of the current. The curl of your fingers indicates the direction of the magnetic dipole moment (\( \vec{\mu} \)).The formula for the magnetic dipole moment \( \vec{\mu} \) of a current loop is:\[ \vec{\mu} = I \cdot (\text{Area Vector}) \]Calculating the Area Vector:If we look closely, the loop is perpendicular to the plane forming a rectangle. The effective area vectors are the summ

Answered: Image /qna-images/answer/4aa130ba-17af-44f9-9621-fb0820ba8ced.jpg

Answered: Find the magnetic dipole moment of the…

Find the magnetic dipole moment of the current loop given in the figure. A) Ia² (-î -ĵ+ k) B) Ia² (-k) C) Ia²(-i-)-k) D) Ia²(-k) E) Ia² (-1)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: We lay a copper wire in the shape of a 10 cm square loop square. The wire has a diameter of 1 mm…

A: In summary;Magnetic moment of the wire loop is = 0.0499 Am^2The maximum torque applied to the loop…

Q: A loop of wire has a magnetic moment of ?=0.042 Am^2 that is towards into the page and is placed in…

Q: nt and (d) the magni tron has m = - 4, w nt and (h) the magn

Q: An electron moves along the z-axis with vz-5.8x107m/s. As it passes the origin, what are the…

A: An electron moves along the z-axis with Vz . As it passes the origin, what are the strength and…

Q: If an electron in an atom haş an orbital angular momentum with m, = 2, what are the components (a)…

Q: (b) An electron and an alpha particle both move in a circular path in a magnetic field with the same…

A: Given: The mass of the electron is me=9.11×10-31 kg. The mass of the alpha particle is…

Q: 1) Consider the particles described below. They all have the same kinetic energy entering a uniform…

A: Solution 1. The charged particle having initial speed in a magnetic field experiences a centripetal…

Q: Consider a simple hydrogen atom where an electron orbits around a proton. Suppose a small magnetic…

Q: If we plot V vs. r² at a constant magnetic field strength of 2T, how would the charge to mass ratio…

Q: If an electron in a particular atom has an orbital magnetic quantum number of 1 , how much energy is…

A: The energy associated with the orientation of an electron's magnetic dipole moment in an external…

Q: A long, coaxial cable, shown in cross-section in the drawing, is made using two conductors that…

Q: An ion source is producing Li ions, which have charge +e and mass 9.99 × 102 kg. The ions are…

A: Given: q=e=1.6x10-19 C m= 9.99x10-27 Kg V= 15KV = 15000V B= 1.6T

Q: (8) (8) b. TB

A: Given: ( reference diagram): The direction of the magnetic field is inside the plane of the page.…

Q: A próton with a net positive charge of 1.6e-19 Coulombs and a mass of 1.67e- 27 kg takes 3 days to…

A: Given a proton with m=1.67×10-27kgq= 1.6×10-19C earths magnetic field B=.5×10-4T

Q: If an electron in an atom has an orbital angular momentum with my = 5, what are the components (a)…

Q: Two concentric, circular wire loops of radii r1 = 18.7 cm and r2 = 26.3 cm, are located in an xy…

Q: A beam of protons is fired into a region of uniform magnetic field with a speed of 80200 m/s. What…

A: When the beam of protons enter into the magnetic field, the Lorentz force will be equal to the…

Q: 29. A hydrogen isotope separator contains positively ionized hydrogen H', with isotope of hydrogen,…

A: Given potential difference ΔV = 200V MD2 = 2×1.67×10-27 kg Q = 1.6×10-19 C

Q: estimate the current that an electric car would have to provide to its motor such that it can do…

A: Given: τ→ = μ→×B→ = IA→×B→Initial speed = u =0 kphFinal speed == v = 100 kphTime = 3sec Magnetic…

Concept explainers

Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

Question

**Finding the Magnetic Dipole Moment \( \vec{\mu} \) of the Current Loop**

Consider the problem statement:

Find the magnetic dipole moment \( \vec{\mu} \) of the current loop given in the figure.

**Options:**
A) \( I a^2 (-\hat{i} - \hat{j} + \hat{k}) \)
B) \( I a^2 \left( \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \)
C) \( I a^2 \left( -\hat{i} - \frac{1}{\sqrt{2}} \hat{j} - \frac{1}{\sqrt{2}} \hat{k} \right) \)
D) \( I a^2 (-\hat{k}) \)
E) \( I a^2 (-\hat{j}) \)

**Explanation of the Diagram:**

The diagram shows a 3D representation of a rectangular loop oriented in the x-y-z coordinate system with a current \( I \) flowing through it.

- The loop is aligned with the coordinate planes such that:
- One surface is parallel to the xz-plane.
- Another surface is parallel to the yz-plane.
- The loop creates a rectangular circuit and the dimensions of the rectangle are given as 'a' for both length and width.

Arrows indicate the direction of the current steadily flowing through the loop:

- \(\hat{x}\): The positive x-direction arrow indicates the current flowing parallel to the x-axis.
- \(\hat{y}\): The positive y-direction arrow indicates the current is flowing parallel to the y-axis.
- \(\hat{z}\): The current is flowing parallel to the z-axis.

Use the right-hand rule: Point the thumb of your right hand in the direction of the current. The curl of your fingers indicates the direction of the magnetic dipole moment (\( \vec{\mu} \)).

The formula for the magnetic dipole moment \( \vec{\mu} \) of a current loop is:
\[ \vec{\mu} = I \cdot (\text{Area Vector}) \]

Calculating the Area Vector:

If we look closely, the loop is perpendicular to the plane forming a rectangle. The effective area vectors are the summ

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given Information -

VIEW

Step 2: Calculation -

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

1 Singly-charged lithium ions, liberated from a heated anode are accelerated by a difference of 400 V between anode and cathode. They then pass through a hole in the cathode into a uniform magnetic field perpendicular to their direction of motion. The magnetic flux density is 8 × 10-2 Wb/m² and the radii of the paths of the ions are 8.83 and 9.54 cm, respectively. Calculate the mass numbers of the lithium isotopes.
Ch. 28
How the Biot-Savart Law Differs from Ampère's Law A current Io flows up the z-axis from z = z, to z = 22 as shown below. %3D Z2 (a) Use the Biot-Savart law to show that the magnetic field in the z = 0 plane is Ho lo {cos 02 – cos 01}6. 4π ρ B(p, 6, 0) = |
(a) An oxygen-16 ion with a mass of 2.66 × 10−26 kg travels at 5.0 × 106m/s perpendicular to a 1.20-T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive charge is on the ion? (b) What is the ratio of this charge to the charge of an electron? (c) Discuss why the ratio found in (b) should be an integer.
Atomic masses 12C 14N 160 12.000 u 14.003 u 15.995 u -19 To five significant figures, what is the cyclotron frequency in a 3.0000 T magnetic field of the ion O₂? The atomic masses are shown in the table; the mass of the missing electron is less than 0.001 u and is not relevant at this level of precision. Use the following constants: 1 u = 1.6605 × 10−27 kg, e = 1.6022 × 10¯ C. Express your answer with the appropriate units. ► View Available Hint(s) fo Submit Part B X Incorrect; Try Again; 14 attempts remaining fN₂ = Value Submit Previous Answers To five significant figures, what is the cyclotron frequency in a 3.0000 T magnetic field of the ion N₂ ? Express your answer with the appropriate units. ► View Available Hint(s) Part C Units Value Units ? Review Although N+ and CO+ both have a nominal molecular mass of 28, they are easily distinguished by virtue of their slightly different cyclotron frequencies. To five significant figures, what is the cyclotron frequency in a 3.0000 T…
Pls help ASAP