A long solenoid has n-turns per unit length, a radius Rl, and carries current I.

Question

A long solenoid has n-turns per unit length, a radius Rl, and carries current I. A circular loop with radius R2 and N total turns is coaxial with the solenoid and equidistant from its ends. Assume the magnetic field due to a solenoid is the approximate formula we derived in class (i.e. constant) inside the solenoid, and zero outside it. Find the magnetic flux through the coil. (Assume that the flux for N turns is N times the flux for a single turn). Get the value for both cases R1R2. Hint: The flux is the magnetic field multiplied by the area that is common between the area the field is present in and the area of the loop itself. Let 1= 10 Amperes, Rl=l cm, R2=0.5 cm, n=1000 turns/meter and N=50. Find the magnitude of the flux (in b)) in Webers.

Explanation / Answer

a) if R1<R2

then flux = N B A = N u0 n I pi R1^2

if R1>R2 then flux = N u0 n I pi R2^2

b) flux = 50*4*pi*10^(-7)*1000*10*0.5E-2^2= 1.57E-5

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