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A nerve signal is transmitted along the long, thin axon of a neuron in a small fish. The transmission occurs as sodium ions (Na+)transfer like tipping dominos across the axon membrane from outside to inside. Each short section of axon gets an excess of about 6.0×108sodiumions/mm.

Determine the E field 4.0 cm from the axon produced by the excess sodium ions on the inside of the axon and an equal number of negative ions on the outside of a 1.0-mm length of axon. The ions are separated by the 8.0×10−9-m-thick axon membrane. Use κ = 81 for the dielectric constant of water.

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Answer:

Electric field is 2.67 x 10⁻⁶ N/C

Explanation:

Charge of Sodium ion, q = 6 x 10^8 x 1.6 x 10^-19 = 9.6 x 10^-11 C

Since;

Electric field, E = 2 kdq / Kr^3

Substituting all given parameters

E = (2 x 9 x 10⁹ x 8 x 10⁻⁹ x 9.6 x 10⁻¹¹) / (81 x 0.04³)

E = 2.67 x 10⁻⁶ N/C

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