B7, General Physics Experiment II c Fall Semester, 2020

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Introduction

Goals

� Measure the permittivity constant (ε0) usingparallel plate capacitors.

� Measure the permeability constant (µ0) usingsolenoids.

� Measure the speed of light (c).

Theoretical Backgrounds

1. Propagation of electromagnetic waveThe speed of light (any electromagnetic wave) invacuum has the exact value:

c = 299 792 458 m/s.

(a) Usually, a wave requires a medium (somematerial) through which or along which totravel.

(b) An electromagnetic wave, including lightwave, does not require any medium. It canpropagate in an empty space.

(c) Speed of light in vacuum is

c =1

√µ0ε0

where µ0 and ε0 are permeability andpermittivity in vacuum respectively.

(d) Light has the same speed regardless of theframe of reference in which it is measured.

(e) Light travels through a medium such as air orglass. In that case the electromagneticproperties of the medium slow down the speedof light as

c→ v =c

n,

where n is the index of refraction of thatmedium.

2. Permeability µ determines the strength of themagnetic field due to a source current. Forexample, the Ampere’s law that describes themagnetic field in a medium reads∮

CB · ds = µienc,

where C is a closed loop and ienc is the currentpassing through the area surrounded by the loopC. In the vacuum it is µ = µ0, where

µ0 = 4π × 1.000 000 000 82(20)× 10−7 H/m.

The relative permeability µr is defined in such away that µ = µrµ0. The µr depends on themagnetic properties of the medium.

3. Permittivity ε determines the strength of theelectric field due to a source charge. For example,the Coulomb’s law that describes the electrostaticforce F2→1 on particle 1 with charge q1 by particle2 with charge q2 in a medium reads

F2→1 =1

4πε

q1q2r2

r̂2→1,

where r is the distance between the two chargedparticles and r̂2→1 is the unit vector directed from2 to 1. In the vacuum the permittivity is ε = ε0,where

ε0 ≡1

c2µ0= 8.854 187 8128(13)× 10−12 F/m.

Except for vacuum ε > ε0. ε = εrε0, where εr isthe relative permittivity and depends on theelectric properties of the medium made of adielectric material. The relative permittivity εr isalso called the dielectric constant.

4. Parallel Plate CapacitorConsider a parallel plate capacitor of crosssectional area A, distance d.

(a) If the space between the two plates is empty,then the capacitance is

C = ε0A

d.

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B7, General Physics Experiment II c Fall Semester, 2020

(b) If the space is filled with a dielectric materialwith the relative permittivity εr, then thecapacitance is modified by

C = εA

d= εrε0

A

d.

5. Capacitive reactance of a capacitor ofcapacitance C at angular frequency ω is

XC =1

ωC.

6. Inductive reactance of an inductor ofinductance L at angular frequency ω is

XL = ωL.

Instrumentation

1. Parallel Plate Capacitor

The resources of each capacitor are as follows.

area (cm2) distance (µm)

A (white) 600 23B (blue) 600 75

2. Solenoid

The resources of each coil are as follows.

number of turns length outer diameter(mm) (mm)

A 930 500 76B 588 300 38

3. Connection

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B7, General Physics Experiment II c Fall Semester, 2020

Experimental Procedure

1. Measurement: Apply AC of frequencies listed inthe Excel file to the capacitors A, B and thesolenoids A, and B.

2. Fit: Fit the V and I plots to sine functions.

3. Data Analysis: Fill out the sheets of the Excelfile to carry out the data analysis to determine µ0,ε0, and c.

4. Speed of Light: Excel Sheet 6 will provide youwith the results for µ0, ε0, and c.

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B7, General Physics Experiment II c Fall Semester, 2020

Name:

Team No. :

Department:

Date :

Student ID:

Lecturer’s Signature :

Discussion (7 points)

Problem 1Problem 2

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B7, General Physics Experiment II c Fall Semester, 2020

Problem 3

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