Explanation Given info: The wood thickness is 1.00 cm , number of turns overwrapped is 500 , energy store in the inductor is 1.82 × 10 − 4 J and the current is 2.00 A . Formula to calculate the energy store in the magnetic field of an inductor is, U B = 1 2 L i 2 (1) Here, U B is the energy store in the magnetic field of an inductor. L is the inductance of the toroidal inductor. i is the current flow in the inductor. Rearrange the equation (1) for L . L = 2 U B i 2 (2) Write the expression for the inductance of the toroidal inductor. L = μ 0 N 2 l A (3) Here, N is the total number of turns. μ 0 is the absolute permeability. l is the length of the inductor. A is the cross sectional area of the inductor. Write the expression for the cross sectional area of the inductor. A = h ( b − a ) Here, h is the thickness of the wood inductor. b is the outer radius of the toroidal inductor. a is the inner radius of the toroidal inductor. Write the expression for the length of the inductor. l = 2 π r (4) Here, r is the mean radius of the inductor. Formula to calculate the mean radius of the inductor is, r = b + a 2 Replace r by b + a 2 in equation (4). l = 2 π ( b + a 2 ) = π ( b + a ) Substitute h ( b − a ) for A and π ( b + a ) for l in equation (3) L = μ 0 N 2 ( h ( b − a ) ) π ( b + a ) (5) Equate equation (2) and equation (5) for same value of L . μ 0 N 2 ( h ( b − a ) ) π ( b + a ) = 2 U B i 2 Simplify the above equation. μ 0 N 2 a ( h ( b a − 1 ) ) π a ( b a + 1 ) = 2 U B i 2 μ 0 N 2 ( h ( b a − 1 ) ) π ( b a + 1 ) = 2 U B i 2 Substitute 4 π × 10 − 7 T ⋅ m / A for μ 0 , 500 for N , 1

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Author: Raymond A. Serway, John W. Jewett

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Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is…

Question

Chapter 31, Problem 41AP

To determine

The ratio ba for a toroidal inductor.

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Chapter 31 Solutions

Physics for Scientists and Engineers

Ch. 31.1 - A coil with zero resistance has its ends labeled a...Ch. 31.2 - Prob. 31.2QQ Ch. 31.3 - Prob. 31.3QQ Ch. 31.4 - Prob. 31.4QQ Ch. 31.5 - (i) At an instant of time during the oscillations...Ch. 31 - Prob. 1P Ch. 31 - Prob. 2P Ch. 31 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 31 - Prob. 4P Ch. 31 - Prob. 5P

Ch. 31 - A toroid has a major radius R and a minor radius r...Ch. 31 - Prob. 7P Ch. 31 - Prob. 8P Ch. 31 - Prob. 9P Ch. 31 - Prob. 10P Ch. 31 - Prob. 11P Ch. 31 - Show that i = Iiet/ is a solution of the...Ch. 31 - Prob. 13P Ch. 31 - You are working as a demonstration assistant for a...Ch. 31 - Prob. 15P Ch. 31 - The switch in Figure P31.15 is open for t 0 and...Ch. 31 - Prob. 17P Ch. 31 - Two ideal inductors, L1 and L2, have zero internal...Ch. 31 - Prob. 19P Ch. 31 - Prob. 20P Ch. 31 - Prob. 21P Ch. 31 - Complete the calculation in Example 31.3 by...Ch. 31 - Prob. 23P Ch. 31 - A flat coil of wire has an inductance of 40.0 mH...Ch. 31 - Prob. 25P Ch. 31 - Prob. 26P Ch. 31 - Prob. 27P Ch. 31 - Prob. 28P Ch. 31 - In the circuit of Figure P31.29, the battery emf...Ch. 31 - Prob. 30P Ch. 31 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 31 - Prob. 32P Ch. 31 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 31 - Prob. 34P Ch. 31 - Electrical oscillations are initiated in a series...Ch. 31 - Review. Consider a capacitor with vacuum between...Ch. 31 - A capacitor in a series LC circuit has an initial...Ch. 31 - Prob. 38AP Ch. 31 - Prob. 39AP Ch. 31 - At the moment t = 0, a 24.0-V battery is connected...Ch. 31 - Prob. 41AP Ch. 31 - You are working on an LC circuit for an experiment...Ch. 31 - Prob. 43AP Ch. 31 - Prob. 44AP Ch. 31 - Prob. 45AP Ch. 31 - At t = 0, the open switch in Figure P31.46 is...Ch. 31 - Review. The use of superconductors has been...Ch. 31 - Review. A fundamental property of a type 1...Ch. 31 - Prob. 49AP Ch. 31 - In earlier times when many households received...Ch. 31 - Assume the magnitude of the magnetic field outside...Ch. 31 - Prob. 52CP Ch. 31 - Prob. 53CP

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