Electric Potential, Potential Difference, and Capacitance

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Electric Potential, Potential Difference, and Capacitance

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Electric Potential, Potential Difference, and Capacitance

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Electric Potential, Potential Difference, and Capacitance

Peter Mitrano

Casey Bruck

Michaela Murr

- Definition - the potential energy per unit charge in an electric field
Big Ideas

- Field Lines
- Field lines point to the direction a positive charge would move in an electric field, and have varying values of electric potential along them approaching 0. When a charge moves across a field line work is done.

- Positive and Negative
- Field Lines point in the direction a positive charge would move in order to get to a potential of 0, whereas a negative charge will move the opposite direction, away from 0 and in the opposite direction field lines are drawn.

- Equipotential Lines
- Always perpendicular to Field Lines and have equal potential along the path of the line. When a charge moves across an equipotential line no work is done.

Equations involving Electric Potential:

V=kq/r V=k(q1/r1+q2/r2+q3/r3….)

a. What is the Electric Potential of a 2 micro-C charge at a distance 10m away.( Answer: V = 1800V)

b. What is the Electric Potential of the system if a second charge of 6 micro-C is placed at a distance of 13m vertically down from the first charge. (Answer: V = 5092.683V)

c. The second charge is moved 5m vertically upward; the electric potential remains constant from the answer to the last problem, and a third charge is added at a distance of 12m. What must be the charge on the new particle in order to maintain the electric potential calculated above? (Answer: q = -1.234 micro-C)

Definition - Difference in electric potential (V) between the final and the initial location of a particle (ΔV = Vf - Vi)

When a charge moves up/down E-field lines, there is a change in its potential energy. Potential difference is the change in energy per unit charge, or

ΔV = ΔUE/q

In a uniform electric field: ΔV = Ed

Units are joules/coulomb, or volts

The change in voltage over distance can be used to find the E-field:

E = -dV/dr

**Electric potential difference (ΔV) is often denoted the same way as electric potential (V)

Scalar quantity because associated with energy change

Potential difference allows charge to move. Charge flows from high potential to low potential.

Emf is the energy per unit charge transferred to the moving charges by the battery

The quantity iR is the energy per unit charge transferred from the moving charges to thermal energy within the resistor

V = iR

If the green dot represents a particle’s

initial position, which red dot indicates

a change in energy? (Equipotential lines

are perpendicular to E-field lines)

In a given lightning flash, the potential difference between the cloud and the ground is 1,000,000,000 V and the quantity of charge transferred is 30 C. What is the decrease in energy of that transferred charge? (ΔV = ΔUE/q)

30,000,000,000 J

The difference in electric potential V in the space between two flat parallel plates is given by V = 1500x^2, where V is in volts if x, the distance from one of the plates, is in meters. Calculate the magnitude and direction of the electric field at x = 1.3 cm. [(-39 V/m) i-hat]

Definition- Capacitance is the storage of electric charge

Relevant Big Ideas:

- Gauss
- Electric Potential
- Charge & Conduction
Shapes we care about

- Parallel Plates
- Cylinders
- Spheres
We’re going to find Voltage across these types, and to do that, we look at E fields

We can use Gauss to find the potential difference across the plates

We can follow the same logic for cylinders and shells

q=CV

(definition of capacitance)

C=eA/d

(geometry)

U=½QV=½CV2

(You have to do work to store charge)

A) What is the equivalent capacitance? (ANSWER: 5.965uF)

B) If Vab is 15v, what is the charge on the 3uF capacitor? (ANSWER: 0.746uC)

C) What is the energy stored in the 15uF capacitor? (ANSWER: 4.174J)