An MRI technician moves her hand from a region of very low magnetic field strength ( approximately zero) into the MRI scanner's field in a quick motion, taking 3.1 milliseconds. The MRI is essentially a solenoid, with 1500 loops of wire. By doing so, a current of 0.15 milliAmps is induced in her wedding ring. If her wedding ring has a diameter of 1.95 cm and it has measured resistance of 119 Ohms, what is the magnetic field in the MRI.
An MRI technician moves her hand from a region of very low magnetic field strength ( approximately zero) into the MRI scanner's field in a quick motion, taking 3.1 milliseconds. The MRI is essentially a solenoid, with 1500 loops of wire. By doing so, a current of 0.15 milliAmps is induced in her wedding ring. If her wedding ring has a diameter of 1.95 cm and it has measured resistance of 119 Ohms, what is the magnetic field in the MRI.
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)...
Related questions
Question
An MRI technician moves her hand from a region of very low magnetic field strength ( approximately zero) into the MRI scanner's field in a quick motion, taking 3.1 milliseconds. The MRI is essentially a solenoid, with 1500 loops of wire. By doing so, a current of 0.15 milliAmps is induced in her wedding ring. If her wedding ring has a diameter of 1.95 cm and it has measured resistance of 119 Ohms, what is the magnetic field in the MRI.
![**Title: Understanding Magnetic Fields in MRI Technology**
**Problem Explanation:**
An MRI technician moves her hand from an area with low magnetic field strength into the field of an MRI scanner. This movement occurs over 3.1 milliseconds. The scenario involves a 0.15-milliamp current induced in a wedding ring, which has a 1.95 cm diameter, being wound with 1500 loops of wire. The ring’s resistance is 119 Ohms. The goal is to determine the magnetic field in the MRI.
**Illustrations:**
- A simple diagram shows a hand moving into an MRI scanner, indicating the directional axes (x, y, z).
- The magnetic field is depicted with lines, and a coil (representing the wedding ring) is shown with loops around a central point.
**Variables and Equations:**
- \(\Delta t = 3.1 \, \text{ms}\)
- \(I = 0.15 \, \text{mA}\)
- \(d = 1.95 \, \text{cm}\)
- \(R = 119 \, \Omega\)
- \(N = 1500\)
- \(B = ?\)
Relevant Equations:
- Ohm's Law: \(V = IR\)
- Electromagnetic Force: \(\mathcal{E} = \frac{\Delta \Phi}{\Delta t}\)
- Magnetic Flux: \(\Phi_i = BA \cos \Theta\)
**Solution Steps:**
1. **Voltage Calculation:**
\[
V = IR = (0.15 \times 10^{-3})(119) = 0.01785 \, \text{V} = \mathcal{E}
\]
2. **Magnetic Flux:**
\[
\Phi_i = BA \cos \Theta = B (\pi (1.95)^2) = 11.9459B
\]
3. **Total Flux:**
\[
\Phi_{\text{tot}} = N \Phi_i = (1500) (11.9459B) = 17918.859B
\]
4. **Electromotive Force:**
\[
\mathcal{E} = \frac{\Delta \Phi}{\Delta t} = \frac{17918.859B}{3.1 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd17be823-b511-4138-b1ab-72ddbf846f2e%2Fd620dec8-3b1c-49d8-ab87-33f73e0e6cbb%2Fn3m7el_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Magnetic Fields in MRI Technology**
**Problem Explanation:**
An MRI technician moves her hand from an area with low magnetic field strength into the field of an MRI scanner. This movement occurs over 3.1 milliseconds. The scenario involves a 0.15-milliamp current induced in a wedding ring, which has a 1.95 cm diameter, being wound with 1500 loops of wire. The ring’s resistance is 119 Ohms. The goal is to determine the magnetic field in the MRI.
**Illustrations:**
- A simple diagram shows a hand moving into an MRI scanner, indicating the directional axes (x, y, z).
- The magnetic field is depicted with lines, and a coil (representing the wedding ring) is shown with loops around a central point.
**Variables and Equations:**
- \(\Delta t = 3.1 \, \text{ms}\)
- \(I = 0.15 \, \text{mA}\)
- \(d = 1.95 \, \text{cm}\)
- \(R = 119 \, \Omega\)
- \(N = 1500\)
- \(B = ?\)
Relevant Equations:
- Ohm's Law: \(V = IR\)
- Electromagnetic Force: \(\mathcal{E} = \frac{\Delta \Phi}{\Delta t}\)
- Magnetic Flux: \(\Phi_i = BA \cos \Theta\)
**Solution Steps:**
1. **Voltage Calculation:**
\[
V = IR = (0.15 \times 10^{-3})(119) = 0.01785 \, \text{V} = \mathcal{E}
\]
2. **Magnetic Flux:**
\[
\Phi_i = BA \cos \Theta = B (\pi (1.95)^2) = 11.9459B
\]
3. **Total Flux:**
\[
\Phi_{\text{tot}} = N \Phi_i = (1500) (11.9459B) = 17918.859B
\]
4. **Electromotive Force:**
\[
\mathcal{E} = \frac{\Delta \Phi}{\Delta t} = \frac{17918.859B}{3.1 \times
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
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.Recommended textbooks for you
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON