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

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

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

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

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that a lot all right for a solid conducting sphere

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with a total charge Plus q and a radius are

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Which plot is the correct representation of the electrical field

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Solid line there and the electrical potential dash line as

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functions of our and here the potential answers Wrong things

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All right we like grafts They bring out our inner

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artist because our inner artist can only draw straight lines

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

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

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It has a charge but that charges all on the

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outside because particles with the same charge repel each other

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

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repulsive like having showered in three days repulsive like that

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So they get us far apart from each other as

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they can on the edge of the sphere which means

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that inside the sphere the charge is neutral and the

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electrical field is zero Well when an electrical field equal

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

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we see an answer be wooden cross that one off

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the list In fact the key to this question is

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looking at the section within the sphere from zero to

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the radius a k a the big r in all

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the grafts the section outside the sphere is the same

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

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field and the equation for the magnitude of an electrical

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potential field are almost the same Well the equation for

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a new electrical field is one over four times pi

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times the constant of electrical primitive ity of free space

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or as we like to call it excellence of zero

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which was not our college fraternity although it could have

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

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charge over the distance squared It was like this worth

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my toga here All right the equation for a new

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

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the square of the distance We just use the distance

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Well these equations give us reciprocal function graphs as we

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see in all of the graph for the space outside

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of the sphere but inside the potential field is constant

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and the electric field is zero The only graph that

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fills those requirements is a right there Remember that electric

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

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

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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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