The current in the circuit is equal to the induced electromotive force E.M.F. divided by the resistance of the loop.
I = Ɛi/R
The electromotive force is calculated by Faraday's law:
Ɛi = ΔфB/∆t
where фB Is the magnetic flux through the loop. The magnetic flux is the total number of field lines, through the area occupied by the loop and has the following value:
фB = B A = B πr^2.
Here, πr^2 is the area of the loop of radius r. The radius of the loop can be computed from the total length of the wire:
2πr = L → r = L/2πr^2 = L^2/4π^2
Evaluating the equation of magnetic flux, we have:
фB = (B π)(L^2/4π^2)
Initially, the magnetic field in the elecroiman is zero. After closing the switch during 14ms, the EMF generated is:
Ɛi = ΔфB/∆t = (BL^2/4π)/t = BL^2/4πt
Ɛi = (0.55)(0.19)^2/4(3.14)(0.014) = 0.113 V
To find the resistance R, we apply the law of Pouillet:R = ρL/S
Where ρ = 10^-6 Ω m, is the resistivity of nichrome, L is the length of wire and S is the area of cross section.
The wire radius is: r = d/2 = (2.7 10^-4)/2 = 1.35 10^-4 m
R = ρL/πr^2 = (10^-6)(0.19)/(3.14)(1.35 10^-4)^2
R = 3.32 Ω
Finally, the current generated is:
I = Ɛi/R = 0.113/3.32 = 0.034 A = 34 mA
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