A nerve signal is transmitted through a neuron when an excess of Na+ ions sudden

Question

A nerve signal is transmitted through a neuron when an excess of Na+ ions suddenly enters the axon, a long cylindrical part of the neuron. Axons are approximately 10.8 m in diameter, and measurements show that about 6.0×1011 Na+ ions per meter (each of charge +e) enter during this process. Although the axon is a long cylinder, the charge does not all enter everywhere at the same time. A plausible model would be a series of nearly point charges moving along the axon. Let us look at a 0.10 mm length of the axon and model it as a point charge.

If the charge that enters each meter of the axon gets distributed uniformly along it, how many coulombs of charge enter a 0.10 mm length of the axon? Q=___C

What electric field (magnitude and direction) does the sudden influx of charge produce at the surface of the body if the axon is 4.80 cm below the skin? E= ___N/C

Certain sharks can respond to electric fields as weak as 1.50 N/C . How far from this segment of axon could a shark be and still detect its electric field? R=____m

Explanation / Answer

long cylindrical part of the neuron
This is good we can use gauss law
because the axon is long
Gauss law requires you to draw a shape best draw a cylinder
Flux=Q/Eo
They give you a linear charge density I will call it y
y=Q/L
yL=Q
Flux=yL/Eo
Eo is the constant
Now
Electric Field=Flux/Area
yL/EoA
Now the surface area of a cylinder is
2piR^2+2piLR
The ends of the cylinder willn't have flux going through cause this axon is super long so the circles willn't have any flux
Total area=2piLR
yL/Eo2piRL
y/Eo2piR
R is the distance we want
y= 6.0×1011 ion/m
now there's a lot of convert with um and uN/C

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