Open-Response Homework Problem 18.1 Consider a large solenoid with parameters tu

Question

Open-Response Homework Problem 18.1 Consider a large solenoid with parameters turns NL, radius RL, and length LL. The solenoid carries a current of IL. Inside the large solenoid is a smaller solenoid with parameters, turns N3, radius R8, and length LS. This would be the situation if I placed the tennis ball can solenoid n the sewer pipe solenoid. In all parts, write the expressions in terms of the quantities given above and the quantities introduced in part (c). (a)[2 Pt(s) ]Calculate the symbolic expression for the magnetic field of the large solenoid. (b)[2 pt(s) ]Calculate the magnetic flux through the small solenoid due to the magnetic field produced by the large solenoid. (c)[4 pt(s) If the current through the large solenoid changes with time by the function IL(t) = I0 sin wt, calculate the emf induced n the small solenoid. (d)[1 pt(s) ]What is the physical law you used in the calculation in (c)? (e)[2 pt(s) ]Calculate the mutual inductance between the large and small solenoid. Note what we have done here is build an air filled step down transformer.

Explanation / Answer

Here ,

a) as the magnetic field due to solenoid is

B = u0*N*I/L

BL = u0*NL*IL/LL

the magnetic field due to larger solenoid is u0*NL*IL/LL

b)

magnetic flux = N * Area * B

magnetic flux through the smaller solenoid = Ns * pi *Rs^2 * u0*NL*IL/LL

the magnetic flux through the smaller solenoid is Ns * pi *Rs^2 * u0*NL*IL/LL

c)

as I = Io * sin(w * t)

dI/dt = Io * w * cos(w*t)

emf induced = rate of change of flux in the smaller solenoid ,

emf induced = d/dt(Ns * pi *Rs^2 * u0*NL*IL/LL)

emf induced = Ns * pi *Rs^2 * u0*NL/LL * dI/dt

emf induced = Ns * pi *Rs^2 * u0*NL*Io * w * cos(w*t) /LL

d)

this is the Faraday's law

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