STUDY GUIDE CHAPTER 23SECTION 5

MSTC Physics C

Mutual Inductance

If 2 coils of wire are placed near one another, a changing I in one will induce an emf in the other

From Faraday ε2 α (dΦ2/dt) where Φ2 is due to I1

N2Φ2 α I1

N2Φ2 = MI1 M = mutual inductance

Therefore ε2 = -N2(dΦ2/dt) = -N2 d/dt(MI/N2) = -M(dI1/dt)[M] = Wb/A = Henry, H

Mutual Inductance

ε2 = -M(dI1/dt)

Mutual inductance depends on - size - shape - number of turns - relative positions of 2 coils - whether a ferromagnetic material is present

Factors That Change Inductance

NUMBER OF WIRE WRAPS, OR "TURNS" IN THE COIL: All other factors being equal, a greater number of turns of wire in the coil results in greater inductance; fewer turns of wire in the coil results in less inductance.

Explanation: More turns of wire means that the coil will generate a greater amount of magnetic field force (measured in amp-turns!), for a given amount of coil current.

Factors That Change Inductance

COIL AREA: All other factors being equal, greater coil area (as measured looking lengthwise through the coil, at the cross-section of the core) results in greater inductance; less coil area results in less inductance.

Explanation: Greater coil area presents less opposition to the formation of magnetic field flux, for a given amount of field force (amp-turns).

Factors That Change Inductance

COIL LENGTH: All other factors being equal, the longer the coil's length, the less inductance; the shorter the coil's length, the greater the inductance.

Explanation: A longer path for the magnetic field flux to take results in more opposition to the formation of that flux for any given amount of field force (amp-turns).

Factors That Change Inductance

CORE MATERIAL: All other factors being equal, the greater the magnetic permeability of the core which the coil is wrapped around, the greater the inductance; the less the permeability of the core, the less the inductance.

Explanation: A core material with greater magnetic permeability results in greater magnetic field flux for any given amount of field force (amp-turns).

Sample Problem

Two coils, held in fixed positions, have a mutual inductance of 100 μH. What is the peak voltage in one of the coils when a sinusoidal current is given by I = (10A) sin (1000t) flows in the other coil?

Sample Problem

A 70 turn solenoid is 5 cm long, 1 cm in diameter, and carries a 2 A current. A single loop of wire, 3 cm in diameter, is help perpendicular to the axis of the solenoid. What is the mutual inductance of the two if the plane of the loop passes through the center of the solenoid?

Self Inductance

Inductance also applies to an isolated single coil of N turns

Changing I in coil produces a Φ in coil that changes and induces an ε that tries to oppose ΔΦ

Like before NΦ α I NΦ = LI L = self

inductance[L] = Henry, H

So ε = - N(dΦ/dt) = -Nd/dt(LI/N) = -L(dI/dt)

Inductor

Coil that has a significant self-inductance

Inductor

Uses?

traffic light sensor Metal detector Stun guns in combination with a capacitor to tune your radio

Sample Problem

A 0.388 mH inductor has a length that is four times its diameter. It if is wound with 22 turns per centimeter, what is its length?

Energy Stored in an Inductor

Inductors store energy

U = ½ L I2

Sample Problem

Calculate the energy associated with the magnetic field of a 200 turn solenoid in which a current of

1.75 A produces a flux of 0.00037 Wb in each turn.

Sample Problem

Two nearby solenoids, A and B, sharing the same cylindrical axis, have 400 and 700 turns, respectively. A current of 3.5 A in coil A produces a flux of 300 μWb at the center of A and a flux of 90 μWb at the center of B. (a) Calculate the mutual inductance of the two solenoids. (b) What is the self inductance of coil A? (c) What emf will be induced in coil B when the current in coil A increases at the rate of 0.5 A/s?