Electromagnetism Assume a nerve of 0.50 m in length is stimulated and sends elec

Question

Electromagnetism Assume a nerve of 0.50 m in length is stimulated and sends electrical impulses to the brain. Along this section of nerve the velocity of the signal is around 0.40 m/s. How long does a signal take to travel the length of the nerve? Assuming the charge traveling through the nerve to be that of 100.0 electrons, what would be the current traveling through the nerve? What would be the magnetic field strength 0.01x103 m away from the nerve? What would the maximum force generated by the current through the nerve be at that same distance? What would be the electric field within the nerve carrying the current?

Explanation / Answer

signal velocity in nerve = v = 0.4 m/s
length of nerve, l = 0.5 m
time taken = t
now, v = l/t
t = l/v = 0.5/0.4 = 1.25 s

number of electrons in the nerve = 100 electrons = n
charge on electron, e = 1.6*10^-19 C
current = charge/time = 100*1.6*10^-19/1.25 = 1.28*10^-17 A

distance from the nerve, d = 0.01*10^-3 m
magnetic field due to a ling current crrying wire at distance d = 2kI/d ( where k = 10^-7)
so, B = 2*10^-7*1.28*10^-17/0.01*10^-3 = 25.6*10^-20 T

force on a current carrying wire in a magentic field = BiL sin(theta)
maximum force, F = B*i*(0.5) = 25.6*10^-20 * 1.28*10^-17 * 0.5 = 1.638*10^-36 N

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