Electromagnetic Induction: Self and Mutual Inductance

An inductor consists of 500 turns of wire of resistance 6.0 Ω wound tightly and uniformly on a toroidal ring of an insulating magneticmaterial with relative permeability μ = 40. The material is linear so μ is independent of the magnetic field. The mean radius of the toroid is 15 cm and the cross sectional area is 1.0 cm2.

(there are 4 parts to this question (fulll quesion in attachment, the first is)

a)
Starting from Ampere's law, calculate the self inductance of the coil, assuming that the cross sectional area of the coil is sufficiently small that we can assume that the magnetic field has constant strength inside the coil.

Please can you fully show your working to help me understand. thank you.

An inductor consists of 500 turns of wire of resistance 6.0 Ω wound tightly and uniformly on a toroidal ring of an insulating magnetic material with relative permeability μ = 40. The material is linear so μ is independent of the magnetic field. The mean radius of the toroid is 15 cm and the cross sectional area is 1.0 cm2.

a)
Starting from Ampere's law, calculate the self inductance of the coil, assuming that the cross sectional area of the coil is sufficiently small that we can assume that the magnetic field has constant strength inside the coil.

The magnetic field inside a long toroid of small cross section is same as in a long solenoid and can be derived using Ampere's law as bellow.

Let the toroid of mean radius r has N turns and carries a current I. Let magnetic field along the central line of the toroid is B. Considering an Amperian loop of radius r, the field at each point of the loop will be B and tangential to the loop.

According to Ampere's law the line integral of the ...

Solution Summary

A good question with four parts to learn Electromagnetic induction.
1. To derive and calculate self-inductance of a toroidal coil. 2 To calculate energy stored. 3 To calculate mutual-inductance. 4 To derive and calculate induced current.

A long solenoid of length 8m with a cross-sectional area of 5.0x10^-5 m^2 contains 52,000 turns.
1) Find the self-inductance of the solenoid, assuming that the core is air.
2) If the current in the winding starts at 0 A and is increased steadily to 1.5 A in a time of 0.20 sec, what is the EMF induced in the solenoid?

A.) Show that the mutualinductance between two coaxial coils separated by a distance z as in figure attatched, one of radius a and N_a turns, and the other of radius b << a and N_b turns is:
pi*mu_0*N_a*N_b*a^2*b^2/[2(a^2 + z^2)^(3/2)]
Calculate the magnetic flux through coil b due to the current through coil a.
B.) H

See attached lab report file.
Please complete the graph for Step 9 under procedures (a graph of Primary Current vs. Galvanometer Deflection using the data from Steps 6 and 7) and provide results and conclusions.
Please answer the four questions, the optional question and exercise.

Find the value of the inductance L shown in the attached diagram.
My Answer:
V=L*d(i)/d(t)
L=V/d(i)/d(t)
V=25cos250t
I=14sin250tmA
d(i)=14cos250t
L1=(25cos250t)/(14cos250t)=25/14=1.7857
Lt=2L+2L+L^2/2L=
2L+2L+1/2L=4.5L
Lt=1.765*(2L+2L+L+L)=
1.765*6L=10.71
L=10.71/4.5=2.38
Final answer: 2.38

1- Find the characteristic impedance for a coaxial cable with an inductance of 64 nH/ft and a capacitance of 43 pF/ft.
2- A coaxial cable has an inner diameter of its outer conductor of 0.5 in. The outer diameter of its inner conductor is 0.1 in. The cable is filled with Teflon. Find the characteristic impedance.
3- A coax

A. A long straight cable with radius R carries a current uniformly distributed through its circular cross section. Find the self-inductance per unit length of the cable. Hint: find B inside and outside, then find energy everywhere and relate to the self-inductance (per unit length)
B. This cable is now modified to have an ins

A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m x 0.55 m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 70° with respect to the normal to the plane of the loop.
(a) If the magnetic field decreases to zero in a time of 0.52 s, what is the magnitud

The mutual inductance between the two circuits shown in FIGURE 2 is
20 nH. It may be assumed that (R1 + R*L1) >> w*L1 and that (R2 + RL2) >> w*L2.
(a) Estimate the crosstalk voltage at the load of circuit B when the signal
source of circuit A is V1 = 100 mV at 1 GHz.
(b) Plot the crosstalk voltage (at the load of circuit