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 10.0 μm in diameter, and measurements show that about 5.60×1011 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 0.100 mm length of the axon and model it as a point charge.
1) What electric field (magnitude and direction) does the sudden influx of charge produce at the surface of the body if the axon is 5.00 cm below the skin? Note that distance to the skin is much greater than the length of the charged axon so that the axon charge is effectiely point-like.,
2) If the charge that enters each meter of the axon gets distributed uniformly along it, how many coulombs of charge enter a 0.100 mm length of the axon? Answer in C

3) the field is directed away from the axon or the field is directed into the axon

Answer 1

Answer:

1.611008 N/C

$8.96\times 10^{-12}\ C$

away

Explanation:

n = Number of charge = $5.6\times 10^{11}$

q = Charge of particle = $1.6\times 10^{-19}\ C$

Gap = $0.1\times 10^{-3}\ m$

r = Distance = 5 cm

The charge is given by

$q=ne\\\Rightarrow q=5.6\times 10^{11}\times 1.6\times 10^{-19}\times 0.1\times 10^{-3}\\\Rightarrow q=8.96\times 10^{-12}\ C$

Charge entering axon is $8.96\times 10^{-12}\ C$

Electric field is given by

$E=\dfrac{kq}{r^2}\\\Rightarrow E=\dfrac{8.99\times 10^9\times 8.96\times 10^{-12}}{5\times 10^{-2}}\\\Rightarrow E=1.611008\ N/C$

The electric field is 1.611008 N/C

The charges in the question are all positive so the electric field is directed away from the axon