Transcript Electric Field and Voltage

5.5 Electric Field and Voltage – Uniform
Field
Electric Field and Voltage – Uniform Field
A small test charge will experience a constant force anywhere between
two charge plates due to the uniform electric field found there.
Remembering the definition of Voltage:
V =
Ep
Q
And:
E =
F
=
Fd
Q
Therefore:
=
F
Q
d
V =
Ed
Q
Electric field strength between
two charged plates:
V
E =
d
{units: V/m = N/C}
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5.5 Electric Field and Voltage – Uniform
Field
Application of Uniform Electric Fields – The Cathode Ray Tube
A cathode ray tube (CRT) is a
special vacuum tube that creates
a focused beam of electrons.
Used in old fashioned TV sets,
monitors and oscilloscopes.
The CRT has two key parts:
1) Accelerating anode to generate a focused beam of electrons
2) Deflecting plates to move the beam of electrons to various places on the screen.
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5.5 Electric Field and Voltage – Uniform
Field
How the beam Is Focused an accelerated
Once the electrons are generated by the heating filament in a CRT, they are accelerated by
an accelerating anode, which is essentially a charged plate with a high voltage (500 V –
1000 V in a classroom model). The potential energy of the electrons in an uniform electric
field causes the electrons to increase speeds as they move across the uniform electric field.
Va =
Where:
Ep
Q
=
Ek
Q
=
1/2mv2
Q
Va = accelerating voltage (V)
m = mass of electron = 9.11 x 10-31 kg
v = maximum speed of electrons (m/s)
Q = charge on electron = 1.6 x 10-19 C
Therefore:
v is proportional to the Va!
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5.5 Electric Field and Voltage – Uniform
Field
How Does the amount of Deflection Depend on Electric Field?
Once the accelerating plates make the electrons travel at a
high speed the deflecting plates are used to deflect or
position the beam of electrons at some point of the screen
of the CRT.
y = 1/2at2
Deflection of beam while in between the deflecting plates:
Newton’s
And:
2nd
Law:
F = EQ
a =
F
m
And:
y =
And:
y =
1Ft2
2m
1EQt2
2m
For a particular CRT and at a certain accelerating voltage, ½, Q, m, and t will remain
constant, which means:
The deflection, y, inside the deflecting plates is
y α Vd
proportional to the deflecting voltage Vd.
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5.5 Electric Field and Voltage – Uniform
Field
How Does the Amount of Deflection Depend on E?
The time for the electron beam to travel
distance x, from deflecting plates to the
screen: t = x/vx.
The beam is deflected by the deflecting plates
and follows a curved path while between the
deflecting plates.
Once the beam of electrons leave the deflecting plates, the beam will follow a straight
line until it reaches the screen. The amount of deflection on the screen is directly
proportional to the amount of deflection inside the deflecting plates.
Therefore the deflection you see on the screen, y ' is directly proportional
to δ (deflection between deflecting plates) and :
y' α Vd
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5.5 Electric Field and Voltage – Uniform
Field
How the deflection, y' on the screen of a CRT depends on accelerating
voltage (Va) and deflecting voltage Vd.
The higher the accelerating voltage the faster the
electrons travel and therefore the less time t the
y'
deflecting voltage will be able to deflect them.
Higher Va means less deflection, y'.
Va
On the other hand, the higher the deflecting
voltage the stronger the force on the electrons,
moving the electrons further off their straight
line path. Higher the Vd the greater the
deflection y'
Vd
Summing it up:
y'
α
Vd
Va
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5.5 Electric Field and Voltage – Uniform Field
Key Questions
In this section, you should understand how to solve the following key questions.
Page 202 – Practice Problem 5.5.1: #2
Page 207 – Quick Check #1 - 3
Page 211 - 213 – Review 5.5 #2,3,5,7, & 11