Let's break this down into two parts:

Part A: Current During Inflow of Na+ Ions

We are given the following information:

• The number of Na+ ions entering the axon per meter: $5.6 \times 10^{11}$ ions.
• The time over which they enter: 10 ms = $10 \times 10^{-3}$ s.
• The charge of each Na+ ion: $+e = 1.60 \times 10^{-19}$ C.

The current $I$ is defined as the rate of flow of charge. To find it, we first calculate the total charge $Q$ that enters the axon, and then use the formula for current:

$I = \frac{Q}{t}$

where:

• $Q = \text{(Number of ions)} \times \text{(Charge per ion)}$
• $t$ is the time in seconds.

Step 1: Calculate the total charge

$Q = (5.6 \times 10^{11} \, \text{ions}) \times (1.60 \times 10^{-19} \, \text{C/ion}) = 8.96 \times 10^{-8} \, \text{C}$

Step 2: Calculate the current

Now that we know the total charge, we can calculate the current by dividing it by the time:

$I = \frac{8.96 \times 10^{-8} \, \text{C}}{10 \times 10^{-3} \, \text{s}} = 8.96 \times 10^{-5} \, \text{A}$

So, the current during the inflow of Na+ ions is $8.96 \times 10^{-5} \, \text{A}$.

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Part B: Magnitude of the Electric Field in a Wire

We are given:

• Resistivity of the wire: $\rho = 3.54 \times 10^{-7} \, \Omega \cdot \text{m}$.
• Cross-sectional area of the wire: $A = 2.33 \, \text{mm}^2 = 2.33 \times 10^{-6} \, \text{m}^2$.
• Current through the wire: $I = 2.00 \, \text{A}$.

To find the electric field $E$, we use Ohm’s law in the form:

$E = \frac{I \cdot \rho}{A}$

Step 1: Calculate the electric field

Substitute the given values:

$E = \frac{(2.00 \, \text{A}) \times (3.54 \times 10^{-7} \, \Omega \cdot \text{m})}{2.33 \times 10^{-6} \, \text{m}^2}$

$E = \frac{7.08 \times 10^{-7} \, \text{V/m}}{2.33 \times 10^{-6}} = 0.304 \, \text{V/m}$

Thus, the magnitude of the electric field in the wire is 0.304 V/m.

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Summary of Results:

• Part A: The current during the inflow of Na+ ions is $8.96 \times 10^{-5} \, \text{A}$.
• Part B: The magnitude of the electric field in the wire is 0.304 V/m.

Would you like more details or have further questions on this? Here are a few more related questions for you to explore:

1. What is the relationship between current and charge in a conductor?
2. How does resistivity affect the electric field in a material?
3. What happens to the current if the number of Na+ ions entering the axon changes?
4. How would the electric field change if the cross-sectional area of the wire was increased?
5. How does the time duration of the Na+ ion inflow affect the overall current?

Tip: Always remember that current is the rate at which charge flows, and electric field is related to the potential difference and resistivity of materials!