The National High Magnetic Field Laboratory once held the world record for creating the strongest magnetic field. Their largest hybrid magnet can produce a constant magnetic field of 45 T. To see if such a strong magnetic field could pose health risks for nearby workers, calculate the maximum acceleration amax the field could produce for Na+ ions (of mass 3.8 x 10-26 kg) in blood traveling through the aorta. The speed of blood is highly variable, but 55 cm/s is reasonable in the aorta.

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**Title: Understanding the Effects of Strong Magnetic Fields on Ion Acceleration in the Human Body**

**Introduction:**
The National High Magnetic Field Laboratory once held the world record for creating the strongest magnetic field. Their largest hybrid magnet can produce a constant magnetic field of 45 Tesla (T). 

**Objective:**
This exercise aims to assess whether such a strong magnetic field could pose health risks for nearby workers by calculating the maximum acceleration (\(a_{\text{max}}\)) that the field could produce for \( \text{Na}^+ \) ions (Sodium ions) in the blood traveling through the aorta.

**Given Data:**
- Magnetic Field Strength (B): 45 T
- Mass of \( \text{Na}^+ \) ions (\(m\)): \(3.8 \times 10^{-26} \) kg
- Speed of blood through the aorta (\(v\)): 55 cm/s (which is reasonable in the aorta but is highly variable)

**Calculation:**
To calculate the maximum acceleration (\( a_{\text{max}} \)) experienced by the \( \text{Na}^+ \) ions in the magnetic field, use the following formula for magnetic force \(F_B\):

\[ F_B = qvB \]

Where:
- \( q \) is the charge of the ion (for \( \text{Na}^+ \), \( q = +1e \), where \( e = 1.6 \times 10^{-19} \) Coulombs)
- \( v \) is the speed of the ion (55 cm/s, converted to meters: 0.55 m/s)
- \( B \) is the magnetic field (45 T)

Since \( F = ma \),

\[ a_{\text{max}} = \frac{F}{m} = \frac{qvB}{m} \]

Fill in the values to find \( a_{\text{max}} \):

\[ a_{\text{max}} = \frac{(1.6 \times 10^{-19} \text{ C})(0.55 \text{ m/s})(45 \text{ T})}{3.8 \times 10^{-26} \text{ kg}} \]

**Result:**
\[ a_{\text{max}} = \boxed{ \hspace{40pt} } \text{ m/s}^2 \]
Transcribed Image Text:**Title: Understanding the Effects of Strong Magnetic Fields on Ion Acceleration in the Human Body** **Introduction:** The National High Magnetic Field Laboratory once held the world record for creating the strongest magnetic field. Their largest hybrid magnet can produce a constant magnetic field of 45 Tesla (T). **Objective:** This exercise aims to assess whether such a strong magnetic field could pose health risks for nearby workers by calculating the maximum acceleration (\(a_{\text{max}}\)) that the field could produce for \( \text{Na}^+ \) ions (Sodium ions) in the blood traveling through the aorta. **Given Data:** - Magnetic Field Strength (B): 45 T - Mass of \( \text{Na}^+ \) ions (\(m\)): \(3.8 \times 10^{-26} \) kg - Speed of blood through the aorta (\(v\)): 55 cm/s (which is reasonable in the aorta but is highly variable) **Calculation:** To calculate the maximum acceleration (\( a_{\text{max}} \)) experienced by the \( \text{Na}^+ \) ions in the magnetic field, use the following formula for magnetic force \(F_B\): \[ F_B = qvB \] Where: - \( q \) is the charge of the ion (for \( \text{Na}^+ \), \( q = +1e \), where \( e = 1.6 \times 10^{-19} \) Coulombs) - \( v \) is the speed of the ion (55 cm/s, converted to meters: 0.55 m/s) - \( B \) is the magnetic field (45 T) Since \( F = ma \), \[ a_{\text{max}} = \frac{F}{m} = \frac{qvB}{m} \] Fill in the values to find \( a_{\text{max}} \): \[ a_{\text{max}} = \frac{(1.6 \times 10^{-19} \text{ C})(0.55 \text{ m/s})(45 \text{ T})}{3.8 \times 10^{-26} \text{ kg}} \] **Result:** \[ a_{\text{max}} = \boxed{ \hspace{40pt} } \text{ m/s}^2 \]
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