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Charge and Energy
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About the lecture
In this first mini-lecture we introduce the concept of a charge in an electric field, focusing in particular on: (i) the equation F = q × Electric Field Strength, where F is the force a change feels in an electric field and q is the charge measured in units of Coulombs (C); (ii) familiar objects that create electric fields; (iii) charges, which are either positive or negative, for example the electron which is negative; (iv) the potential energy = Fd, where F is a constant force and d is the distance travelled; (v) the potential difference, or voltage, which is the potential energy per unit charge in some electric field and is measured in units of volts (V); (vi) the energy (E), or ‘work done,’ which is given by E = qv; and (vii) a couple of examples that use E = qv.
About the lecturer
David Berman is a Professor of Theoretical Physics at Queen Mary. His research interests include string theory and ideas in fundamental theoretical physics, including non-commutative geometry, black holes physics, and quantum gravity. He has contributed to the Radio 4 biography series Great Lives and the In Our Time podcasts, including Great Lives: Richard Feynman (2018), Great Lives: Galileo (2019), In Our Time: Emmy Noether (2019), and In Our Time: Paul Dirac (2020).
Hello.
00:00:06My name is Professor David Berman
00:00:07at Queen Mary
00:00:09University of London.
00:00:11Today
00:00:13I'm going to talk to you
00:00:15about circuits
00:00:16and electricity,
00:00:17and I'm going to start with this mini lecture on charge and energy.
00:00:19So
00:00:26let's begin
00:00:27with what are the charges?
00:00:28A charge is something
00:00:30that feels and responds to
00:00:33an electric field.
00:00:35In other words,
00:00:37it feels a force when it's in an electric field.
00:00:38So
00:00:43we can write it
00:00:44as an equation
00:00:45that the force
00:00:55is equal to
00:00:57the charge
00:00:59times,
00:01:00the electric
00:01:01field
00:01:03strength.
00:01:06We won't be using electric fields much in this course,
00:01:10but it's good to have an idea that this is what charges respond to.
00:01:13And this is what causes the force
00:01:18of electromagnetism,
00:01:20things that create electric fields,
00:01:22that we will see
00:01:25batteries,
00:01:30uh, electric generators,
00:01:32um,
00:01:39and also things like solar cells
00:01:40and a whole host of other things which give us electrical power.
00:01:44Now,
00:01:48what are the units for charge?
00:01:49Charge
00:01:51is measured
00:01:53in
00:01:56columns,
00:01:57which
00:02:00we use. The symbol C
00:02:02importantly
00:02:05charge
00:02:07can be both
00:02:08positive and negative.
00:02:09Okay,
00:02:12can
00:02:13be
00:02:14positive
00:02:16and negative.
00:02:19What does that mean?
00:02:22It means
00:02:24that in a given electric field
00:02:25one charge
00:02:28will move one way
00:02:29and a negative charge
00:02:31with the same value
00:02:33will move in the opposite direction.
00:02:34Okay,
00:02:37now
00:02:39let's look at something that's electrically charged
00:02:41that maybe you've heard of
00:02:43an electron.
00:02:45This is a fundamental particle
00:02:48and is really
00:02:50the smallest charged object there is.
00:02:51It has minus 1.6
00:02:59times 10 to the negative 19 columns.
00:03:02That's no point.
00:03:07No, no, not where I've got 90 knots. 16. Coghlan's
00:03:09very small.
00:03:13Okay,
00:03:15now,
00:03:16if there is a force,
00:03:20there is also
00:03:23a potential energy.
00:03:24So it force
00:03:26implies
00:03:29that there is a potential
00:03:31energy.
00:03:36Okay,
00:03:39And we can work that out because
00:03:41it's going to be related to the work that can be done.
00:03:44Okay.
00:03:48And that will be
00:03:53the force
00:03:55times
00:03:56the distance.
00:03:57This is when we just have a constant force,
00:04:00which is the only things we'll deal with in this course.
00:04:02Now,
00:04:06what that means
00:04:07is that we can, right?
00:04:09This is the charge multiplied by the electric field
00:04:10multiplied by the distance.
00:04:20But
00:04:25often
00:04:26it's useful to think
00:04:27of the potential energy
00:04:29per unit charge.
00:04:31Okay, so we think of something which is the potential energy
00:04:33four
00:04:40a unit charge,
00:04:42meaning
00:04:47the potential energy
00:04:48of one column,
00:04:50so
00:04:52that will equal
00:04:53the potential energy
00:04:54divided by
00:05:00the charge.
00:05:02And it's this
00:05:05which is sometimes called
00:05:06the potential difference
00:05:09or
00:05:18the voltage.
00:05:20So the voltage
00:05:24is the potential energy
00:05:26experienced
00:05:31by one column
00:05:35in some electric field,
00:05:36and it's measured
00:05:42in vaults
00:05:44Now.
00:05:55What that means
00:05:57is that we can write
00:05:59the energy
00:06:01or work done
00:06:05of
00:06:09a particle
00:06:10in
00:06:13an electric field
00:06:15will be equal to
00:06:21the charge
00:06:23times the voltage.
00:06:24As usual, we can rearrange this formula in different ways.
00:06:27So to help us remember how to do that,
00:06:31we're going to construct a triangle
00:06:34for this algebraic relation.
00:06:36We will have energy e at the top.
00:06:40Q.
00:06:43The bottom left
00:06:44V on the bottom right,
00:06:46and we will form a little pyramid
00:06:49that will help us
00:06:52remember all the different ways we can rearrange this equation
00:06:54so we can have
00:06:58Q
00:07:00E divided by V
00:07:01E
00:07:06equal to Q
00:07:08times V
00:07:10M V
00:07:15equal to e over. Q.
00:07:16Then
00:07:24we can do lots of different examples
00:07:25showing how
00:07:28the energy
00:07:29and charge
00:07:31related to the voltage.
00:07:32Now, let's do some examples
00:07:35so we can see how to use these formula.
00:07:37Let's think of a six volt battery,
00:07:41one cool in charge
00:07:47and ask,
00:07:51How much energy
00:07:53does the battery give to that charge?
00:07:54Well, the energy
00:08:13will be cute
00:08:15Times V,
00:08:16which in this case Q is one
00:08:18b six.
00:08:21So you'll get six fuels
00:08:23from this battery
00:08:25for this single cooling with charge.
00:08:27Let's do one more
00:08:33example.
00:08:34Let's think about lightning
00:08:36so
00:08:39lightning
00:08:40actually
00:08:42has associated to it a potential difference
00:08:44of 30 million
00:08:47faults.
00:08:49That's a lot.
00:08:53Interestingly,
00:08:56the total amount of charge that moves in a lightning bolt.
00:08:57It's not as much as you might think.
00:09:00The charge that moves
00:09:02is
00:09:08around 15 columns,
00:09:08not quite so much.
00:09:11But let's see how much energy
00:09:13is in that lightning bolt
00:09:15again. E
00:09:18is Q. Times V
00:09:19will equal
00:09:2215
00:09:24times 300 million,
00:09:26and that will give us
00:09:324500
00:09:34million
00:09:38jewels.
00:09:39Or we can write it as 4500
00:09:41mega jewels.
00:09:44That's the energy in a lightning bolt
00:09:46in this section
00:09:49we've seen that charge
00:09:50is about
00:09:53objects
00:09:54that respond
00:09:55and move under a force
00:09:57in an electric field.
00:09:59We've seen that charges can both positive and negative
00:10:01and
00:10:05we've related the charge
00:10:05to the potential difference of the electric field,
00:10:07which is the potential energy
00:10:11per unit charge.
00:10:13And then
00:10:15we've worked out
00:10:16how we can relate
00:10:17energy
00:10:18charge
00:10:19and voltage.
00:10:20
Cite this Lecture
APA style
Berman, D. (2022, January 12). Module 4: Electricity and Magnetism - Charge and Energy [Video]. MASSOLIT. https://massolit.io/options/module-4-electricity-and-magnetism?auth=0&lesson=4461&option=16825&type=lesson
MLA style
Berman, D. "Module 4: Electricity and Magnetism – Charge and Energy." MASSOLIT, uploaded by MASSOLIT, 12 Jan 2022, https://massolit.io/options/module-4-electricity-and-magnetism?auth=0&lesson=4461&option=16825&type=lesson