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 Ns, radius Rs, and length Ls. This would be the situation if I placed the tennis ball can solenoid in 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 omega t, calculate the ern f induced in 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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