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AP Physics 2: 2.4 Fields in Space
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AP Physics 2: 2.4 Fields in Space. Which plot is the correct representation of the electric field and electric potential as functions of r?

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AP Physics 2: 2.4 Fields in Space 167 Views


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AP Physics 2: 2.4 Fields in Space. Which plot is the correct representation of the electric field and electric potential as functions of r?

Language:
English Language

Transcript

00:00

Thank you We sneak And here's your shmoop du jour

00:05

brought to you by potential We've been told we have

00:08

a lot of potential but only by people who haven't

00:11

seen is pushing on a door marked hole We've done

00:14

that a lot all right for a solid conducting sphere

00:17

with a total charge Plus q and a radius are

00:21

Which plot is the correct representation of the electrical field

00:25

Solid line there and the electrical potential dash line as

00:29

functions of our and here the potential answers Wrong things

00:37

All right we like grafts They bring out our inner

00:40

artist because our inner artist can only draw straight lines

00:43

Curve our inner artist wealth was terrible but let's look

00:46

at the physics involved here We've got a conducting sphere

00:49

It has a charge but that charges all on the

00:52

outside because particles with the same charge repel each other

00:57

So all the charged particles run away because they're really

01:00

repulsive like having showered in three days repulsive like that

01:04

So they get us far apart from each other as

01:06

they can on the edge of the sphere which means

01:09

that inside the sphere the charge is neutral and the

01:13

electrical field is zero Well when an electrical field equal

01:17

zero the potential field is constant it's not rising as

01:20

we see an answer be wooden cross that one off

01:23

the list In fact the key to this question is

01:25

looking at the section within the sphere from zero to

01:28

the radius a k a the big r in all

01:31

the grafts the section outside the sphere is the same

01:34

that's because the equation for the magnitude of an electric

01:36

field and the equation for the magnitude of an electrical

01:39

potential field are almost the same Well the equation for

01:43

a new electrical field is one over four times pi

01:46

times the constant of electrical primitive ity of free space

01:49

or as we like to call it excellence of zero

01:52

which was not our college fraternity although it could have

01:55

been a good one All right that's multiplied by the

01:58

charge over the distance squared It was like this worth

02:01

my toga here All right the equation for a new

02:05

electric potential field is the same except we don't use

02:08

the square of the distance We just use the distance

02:12

Well these equations give us reciprocal function graphs as we

02:15

see in all of the graph for the space outside

02:18

of the sphere but inside the potential field is constant

02:22

and the electric field is zero The only graph that

02:25

fills those requirements is a right there Remember that electric

02:30

potential is constant when there's no electric field and inside

02:33

of conducting sphere there's no electric field and we'll try

02:36

to remember that there may be a reason the door 00:02:39.333 --> [endTime] we're pushing on is an opening

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