Example: A positively charged (+ q ) metal sphere of radius r a is inside

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# Example: A positively charged (+ q ) metal sphere of radius r a is inside - PowerPoint PPT Presentation

Our first exam is next Tuesday - Sep 27. It will cover everything I have covered in class including material covered today. There will be two review sessions Monday, Sep 26 - at 12:30 PM and at 3:00 PM in the same room as the problem solving session: FN 2.212.

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Our first exam is next Tuesday - Sep 27. It will cover everything I have covered in class including material covered today.

There will be two review sessions Monday, Sep 26 - at 12:30 PM and at 3:00 PM in the same room as the problem solving session: FN 2.212.

I have put several (37) review questions/problems on Mastering Physics. These are not for credit but for practice. I will review them at the review session Monday.

of another metal sphere (-q) of radius rb. Find potential at different points

inside and outside of the sphere.

-q

1

a)

2

+q

Total V=V1+V2

b)

c)

Electric field between spheres

Equipotential Surfaces
• Equipotential surface—A surface consisting of a continuous distribution of points having the same electric potential
• Equipotential surfaces and the E field lines are always perpendicular to each other
• No work is done moving charges along an equipotential surface
• For a uniform E field the equipotential surfaces are planes
• For a point charge the equipotential surfaces are spheres

Equipotential Surfaces

Potentials at different points are visualized by equipotential surfaces (just like E-field lines).

Just like topographic lines (lines of equal elevations).

E-field lines and equipotential surfaces are mutually perpendicular

Definitions cont
• Electric circuit—a path through which charge can flow
• Battery—device maintaining a potential difference V between its terminals by means of an internal electrochemical reaction.
• Terminals—points at which charge can enter or leave a battery
Definitions
• Voltage—potential difference between two points in space (or a circuit)
• Capacitor—device to store energy as potential energy in an E field
• Capacitance—the charge on the plates of a capacitor divided by the potential difference of the plates C = q/V
• Farad—unit of capacitance, 1F = 1 C/V. This is a very large unit of capacitance, in practice we use F (10-6) or pF (10-12)
Capacitors
• A capacitor consists of two conductors called plates which get equal but opposite charges on them
• The capacitance of a capacitor C = q/V is a constant of proportionality between q and V and is totally independent of q and V
• The capacitance just depends on the geometry of the capacitor, not q and V
• To charge a capacitor, it is placed in an electric circuit with a source of potential difference or a battery

CAPACITANCE AND CAPACITORS

Capacitor: two conductors separated by insulator and charged by opposite and equal charges (one of the conductors can be at infinity)

Used to store charge and electrostatic energy

Superposition / Linearity: Fields, potentials and potential differences, or voltages (V), are proportional to charge magnitudes (Q)

(all taken positive, V-voltage between plates)

CapacitanceC (1 Farad = 1 Coulomb / 1 Volt) is determined by pure geometry (and insulator properties)

1 Farad IS very BIG: Earth’s C < 1 mF

Calculating Capacitance
• Put a charge q on the plates
• Find E by Gauss’s law, use a surface such that
• Find V by (use a line such that V = Es)
• Find C by

Parallel plate capacitor

Energy stored in a capacitor is related to the E-field between the plates

Electric energy can be regarded as stored in the field itself.

This further suggests that E-field is the separate entity that may exist alongside charges.

Generally, we find the potential difference

Vab between conductors for a certain

charge Q

Point charge potential difference ~ Q

This is generally true for all capacitances

Capacitance configurations

Cylindrical capacitor

Spherical Capacitance

Definitions
• Equivalent Capacitor—a single capacitor that has the same capacitance as a combination of capacitors.
• Parallel Circuit—a circuit in which a potential difference applied across a combination of circuit elements results in the potential difference being applied across each element.
• Series Circuit—a circuit in which a potential difference applied across a combination of circuit elements is the sum of the resulting potential differences across each element.

Capacitors in Parallel

Example: Voltage before and after