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Transcript
ELECTRIC POTENTIAL ENERGY ELECTRIC ENERGY Since the fields are similar between gravitational and electric energy; both are inversed squared force fields This represents the amount of energy to bring the charge to a radius of infinity (if repulsion) or 0 (if attraction) We can use a similar relationship for energy: 𝐸𝐸 = 𝑘𝑞1 𝑞2 𝑟 𝐸𝑔 = 𝐺𝑀𝑚 𝑟 Include sign of charge, negative value indicate attraction, positive value indicate repulsion ELECTRIC POTENTIAL (V) Value of potential energy per unit positive charge Represents work required to move a positive charge at rest at infinity to at rest at another point in the field Attractive - Energy required to remove to stop (-) Repulsive – Energy required to pull in in from ∞ (+) 𝑉= 𝐸𝐸 𝑞 𝑜𝑟 𝑉 = 𝑘𝑞1 𝑟 or 𝐸𝐸 =qV Units: J/C At r=o, Energy is large positive value Very close, lot’s of stored energy because it is ready to be pushed away with a lot of force At r= infinity, energy is small positive value, very little potential to be pushed At r=o, Energy is large negative value Very close, requires lot’s of external energy to be pushed away to infinity At r= infinity, energy is small negative value, very little energy required to be pushed further away VOLTAGE IS…. Energy per unit charge (per coulomb) You can create the analogy… It is Energy per electron ELECTRIC POTENTIAL DIFFERENCE (∆V) Work (change in energy) required to move a charge from one point to another in an electric field Current (flow of charge) redirects charge until electric potential reaches zero Current flows downhill Electron flow is from negative to positive BATTERY • The battery maintains a potential difference • A charge escalator - maintains a charge separation • An electric field is created inside the wire • The electric field strength applies a force on the electrons which generates a current • Moves from a higher potential to a lower potential (- to +) • FMI : http://www.phy-astr.gsu.edu/cymbalyuk/Lecture16.pdf DERIVE ∈= ∆𝑉 𝑑 This equation only applies for a constant electric field as seen between two parallel plates Only a constant electric field because of the evenly spread electric charge over the plate, the field within is changed from an inverse squared force field to a linear squared force field Derivation for a infinite line wire: http://faculty.wwu.edu/vawter/PhysicsNet/Topics/ElectricForce/LineChargeDer.html Since there is an attractive and repulsive field and there is a linear relationship, the sum of the attractive and repulsive forces are a constant DERIVE ∆𝑉 = 1 𝑘𝑞( 𝑟𝐵 − 1 ) 𝑟𝐴 Applies for a point charge in an electric field NOTE W = ∆Ee Work can also be used to produce kinetic energy as ∆Ee=∆Ek EXAMPLE Calculate the electric potential at a distance of 0.80m from a spherical point charge of +8.9µC. Ans: V = +1.0 x 105 V EXAMPLE Find the plate separation for two parallel plates that have an electric potential difference of 120V and produces an electric field of 960N/C. Ans: r = 0.125m EXAMPLE How much work is done to increase the potential of a charge of 15µC with 120V? Ans: W = 1.8 x 10-3J EXAMPLE Two spheres are located 0.80m from each other. Sphere X has a charge of -8.1 x 10-4C but sphere Y has a charge of -1.68 x 10-4C and is free to move. Both spheres have a mass of 1.0 x 10-2 kg. How fast is sphere Y moving when it is 1.5m from sphere X? Ans: 3.8 x 102 m/s