## Let's go back to junior physics for a second :) ## Let's go back to junior physics for a second :) ## What is gravitational potential energy? - Energy that depends on an object's mass and its position relative to some point
- i.e. To calculate someone's potential energy relative to the surface of the Earth you'd need mass, g and height above the surface
## The idea of electric potential energy is similar to that of gravitational potential energy ## The idea of electric potential energy is similar to that of gravitational potential energy - Electric potential energy for a charge is calculated based on the magnitude of the charge and its position relative to some point
## Let's say you have an electric field of magnitude 4500 N/C pointing toward the right ## Let's say you have an electric field of magnitude 4500 N/C pointing toward the right ## If you place a proton in that field, what is the magnitude and direction of the force acting on that proton?
## So since the **force **acting on the proton is toward the right, it will **accelerate** toward the right ## So since the **force **acting on the proton is toward the right, it will **accelerate** toward the right ## What will happen to the proton's kinetic energy and electric potential energy? - Kinetic Energy will increase
- EPE will decrease (conservation of energy)
## Let's say we've got two charged plates that are separated by a small distance (this is a capacitor) ## Let's say we've got two charged plates that are separated by a small distance (this is a capacitor) ## The E-field points from left to right
## A proton between these two plates would move towards the negative plate (right) ## A proton between these two plates would move towards the negative plate (right) ## An electron between these two plates would move towards the positive plate (left)
## A proton has the highest potential energy when it's near the positive plate ## A proton has the highest potential energy when it's near the positive plate ## An electron has the highest potential energy when it's near the negative plate
## By convention, the positive plate is at a higher potential than the negative plate ## By convention, the positive plate is at a higher potential than the negative plate - Positively charged objects move from higher potential to lower potential (i.e. towards negative plate)
- Negatively charged objects move from lower potential to higher potential (i.e. towards positive plate)
## Electric Potential, V, is the potential energy per unit charge - Unit is Volts (1 V= 1J/1 C)
## If a point charge, q, has an electric potential energy at some point a, then the electric potential is
## The change in potential energy of a charge, q, when moved between two points a and b ## The change in potential energy of a charge, q, when moved between two points a and b ## ΔPE = PEb-PEa=qVba
## An electron in a television set is accelerated from rest through a potential difference Vba=+5000 V ## An electron in a television set is accelerated from rest through a potential difference Vba=+5000 V - What is the change in PE of the electron?
- What is the speed of the electron as a result of the acceleration?
- Repeat for a proton that accelerates through a potential difference of -5000 V
## ΔPE = Peb-PEa=qVba ## ΔPE = Peb-PEa=qVba ## ΔPE = qVba=(-1.6 x 10-19 C)(5000 V) ## ΔPE = -8 x 10-16 J - Potential Energy was lost!
## Conservation of Energy! ## Conservation of Energy! - The amount of PE lost, must be equal to the amount of KE gained!
## KE= 8 x 10-16 J=0.5mv2 ## V=4.2 x 107 m/s
## ΔPE = qVba=(1.6 x 10-19 C)(-5000 V) ## ΔPE = qVba=(1.6 x 10-19 C)(-5000 V) ## ΔPE = -8 x 10-16 J (Same as electron) ## Velocity is less because speed is greater ## V=9.8 x 105 m/s
## Since potential energy is always measured relative to some other point, only **differences** in potential energy are measurable ## Since potential energy is always measured relative to some other point, only **differences** in potential energy are measurable - Potential Difference is also known as
**voltage**
## In order to move a charge between two points a and b, the electric force must do work on the charge ## In order to move a charge between two points a and b, the electric force must do work on the charge ## Vab=Va-Vb= -Wba/q - The potential difference between two points a and b is equal to the negative of the
**work done by the electric force** to move the charge from point b to point a, divided by the charge
## How much work is needed to move a proton from a point with a potential of +100 V to a point where it is -50 V? ## How much work is needed to move a proton from a point with a potential of +100 V to a point where it is -50 V?
## We're moving the proton from +100 V to -50 V ## We're moving the proton from +100 V to -50 V - Therefore point A is +100 V, point B is -50 V
## We're looking for the work done by the field ## -Wba= qVab=q(Va-Vb) ## -Wba= (1.6 x 10-19 C)(100V -(-50V)) ## Wba= -2.4 x 10-17 J
## For two parallel plates, the relationship between electric field and electric potential is below ## For two parallel plates, the relationship between electric field and electric potential is below ## E=Vba/d - d is the distance between the plates
## The electron volt is another unit for energy ## The electron volt is another unit for energy ## 1 ev= 1.6 x 10-19 J ## Problem: A proton has 2 MeV of kinetic energy, how fast is it moving? ## 2 x106 eV= 3.2 x 10-13 J= 0.5mv2 ## V= 1.96 x 107 m/s
## Equipotential lines are used to represent electric potential ## Equipotential lines are used to represent electric potential ## Equipotential lines are always perpendicular to electric field lines
## Equipotential lines (green) are perpendicular to the electric field lines (red) ## Equipotential lines (green) are perpendicular to the electric field lines (red)
## The electric potential at a distance r from a single point charge q is : V=kQ/r ## The electric potential at a distance r from a single point charge q is : V=kQ/r - Potential is zero at infinity
## The potential near a negative charge is negative and increases toward zero at large distances ## The potential near a negative charge is negative and increases toward zero at large distances
## What minimum work is required by an external force to bring a charge q = 3.00 microC from a great distance away to a point 0.500 m from a charge Q= 20.0 microC? ## What minimum work is required by an external force to bring a charge q = 3.00 microC from a great distance away to a point 0.500 m from a charge Q= 20.0 microC?
## Basically, we're taking the charge q from a place of zero potential, to a place of nonzero potential ## Basically, we're taking the charge q from a place of zero potential, to a place of nonzero potential ## Use our trusty equation:Vab=Va-Vb= -Wba/q
## The charge is coming from infinity, so Va=0 ## The charge is coming from infinity, so Va=0 ## What is Vb? - Vb=KQ/r=(9x109 Nm2/C2)(20x10-6C)/0.500m
- Vb= 360,000 V
## Wba= -q(Va-Vb)=-(3.00x10-6C)(0-360000V) ## W= 1.08 J
## Electric fields are vectors, but electric potential is a scalar! ## Electric fields are vectors, but electric potential is a scalar! ## When determining the electric potential at a point you can just add the electric potential from each charge, just be sure to include the correct sign of the charge when calculating potential
## Calculate the electric field at a point midway between a -0.5 microC charge and a -0.8 microC charge that are separated by 0.50 m. ## Calculate the electric field at a point midway between a -0.5 microC charge and a -0.8 microC charge that are separated by 0.50 m. ## For the -0.5 microC charge, E= 72000 N/C left ## For the -0.8 microC charge, E= 115,200 N/C right ## Therefore E is 43200 N/C right
## Calculate the electric potential at a point midway between a -0.5 microC charge and a -0.8 microC charge that are separated by 0.50 m. ## Calculate the electric potential at a point midway between a -0.5 microC charge and a -0.8 microC charge that are separated by 0.50 m. ## For the -0.5 microC charge, ## V=kQ/r= (9x109 Nm2/C2)(-0.5 x 10-6 C)/0.25m ## V= -18000 N/C
## For the -0.8 microC charge, ## For the -0.8 microC charge, ## V=kQ/r= (9x109 Nm2/C2)(-0.8 x 10-6 C)/0.25m ## V= -28800 V ## Total V= -46800 V - This is much easier! No directions...just make sure you include the sign!
## A capacitor stores electric charge and consists of two conducting objects that are placed next to each other but not touching ## A capacitor stores electric charge and consists of two conducting objects that are placed next to each other but not touching
## If a voltage is applied to a capacitor (i.e. connected to a battery), then it becomes charged ## If a voltage is applied to a capacitor (i.e. connected to a battery), then it becomes charged ## Amount of charge for each plate: - C= Capacitance of the capacitor (different for each capacitor)
- Unit for C is farad (F)
## A= Area of plates ## A= Area of plates - If A increases, C increases
## d= distance between the plates ## ε0 = 8.85 x 10-12 C2/Nm2 ## (This is the permitivity of free space)
## A charged capacitor stores electric energy ## A charged capacitor stores electric energy
## A 7.7 µF capacitor is charged by a 125 V battery and then is disconnected from the battery. When this capacitor (C1) is connected to a second, uncharged capacitor (C2), the voltage on the first drops to 15 V. What is the value of C2? (Charge is conserved) ## A 7.7 µF capacitor is charged by a 125 V battery and then is disconnected from the battery. When this capacitor (C1) is connected to a second, uncharged capacitor (C2), the voltage on the first drops to 15 V. What is the value of C2? (Charge is conserved)
## For the first capacitor: ## For the first capacitor: ## When the capacitors are connected, the voltage on the first one is 15 V. That means the new charge on C1 is:
## What happens to the rest of the charge? ## What happens to the rest of the charge? - It must be on capacitor 2 because charge is conserved
- Since the two capacitors are connected, the voltage for the second one must also be 15 V
## Capacitors can be connected in series or parallel ## Capacitors can be connected in series or parallel ## When capacitors are connected in parallel, the equivalent capacitance is the sum ## The voltage across each capacitor is the same
## If the capacitors are connected in series, the equivalent capacitance is given by the following expression ## If the capacitors are connected in series, the equivalent capacitance is given by the following expression
## For capacitors in series, the total voltage must equal the sum of the voltages across each capacitor ## For capacitors in series, the total voltage must equal the sum of the voltages across each capacitor ## The charge on each capacitor is the same as the charge on the equivalent capacitor for capacitors in series
## What is the equivalent capacitance for this combination of capacitors? ## What is the equivalent capacitance for this combination of capacitors? ## C2 and C3 are connected in parallel - Combine them into one capacitor
## C23=C2 + C3 = 35 µF
## C23 and C1 are connected in series ## C23 and C1 are connected in series
## How much charge is stored on each capacitor? ## How much charge is stored on each capacitor? - Q=CV
- V1= 50 V (this is the voltage across C1)
## C1 and C23 are connected in series, therefore the charge on C23 is the same as the charge on C1 ## C1 and C23 are connected in series, therefore the charge on C23 is the same as the charge on C1
## C2 and C3 are connected in parallel, therefore: ## C2 and C3 are connected in parallel, therefore: -
## The charge on C2 is: ## The charge on C2 is: ## The charge on C3 is:
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