You have developed a magnetic bacterium that feeds off of magnetic energy. To ke

Question

You have developed a magnetic bacterium that feeds off of magnetic energy. To keep the critters alive they must reside in a magnetic field of at least 0.01 Tesla. Design a bacteriological "holding tank" solenoid of length 1 meter and radius 2 cm to have a magnetic field strength of 0.01 Tesla at its center when carrying a current of 1 Ampere. (a) If the turns are closely spaced with just enough spacing to avoid electrical shorts between adjacent wires, what is the approximate diameter of the wire used to wind the solenoid? (b) What is the self-inductance of this solenoid? (c) What AWG gauge wire would you use to assemble your solenoid? (The solenoid can only have a single layer of turns to prevent over-heating.)

Explanation / Answer

Here ,

magnetic field , B = 0.01 T

length . L = 1 m

let the number of turns is N

as the magnetic field = u0*N*I/L

0.01 = 4pi *10^-7 * N * 1/1

solving for N

N = 7957.75

the number of turns is 7958

diameter of wire = 1/7958 m

diameter of wire = 1.257 *10^-4 m

diameter of wire = 0.1257 mm

the diameter of wire is 0.1257 mm

b)

for the self inductance ,

self inductance = u0*N^2*A/L

self inductance = u0*7958^2 *pi*0.02^2/1

self inductance = 0.1 H

the self inductance is 0.1 H

c)

for mm to AWG

diameter of wire = 36 AWG

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