One method for measuring the magnetic susceptibility of a sample uses an LC circ

Question

One method for measuring the magnetic susceptibility of a sample uses an LC circuit consisting of an air-core solenoid and a capacitor. The resonant frequency of the circuit without the sample is determined and then measured again with the sample inserted in the solenoid. Suppose you have a solenoid that is 5.00 cm long, is 2.60 mm in diameter, and has 500 turns of fine wire. You have a sample that is inserted in the solenoid and completely fills the air space. Neglect end effects (a) Calculate the inductance of the empty solenoid. (b) What value for the capacitance of the capacitor should you choose so that the resonance frequency of the circuit without a sample is exactly 6.0000 MHz? PF (c) When a sample is inserted in the solenoid, you determine that the resonance frequency drops to 5.9989 MHz. Use your data to determine the sample's susceptibility

Explanation / Answer

l = 5.0 cm = 0.05 m

R = 1.3 mm = 1.3*10^-3 m

A = pi*R^2 = 5.3*10^-6 m^2

N = 500

a) Inductance = L = (uo*N^2*A)/l = (4pi*10^-7*500*500*5.3*10^-6)/0.05 = 33.3 uH

b) f = 1/[2pi*sqrt(LC)] ========> C = (1/2pi*f)^2/L

C = (1/2pi*6*10^6)^2/33.3*10^-6 = 21.1 pF

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.