CAPACITANCE III

RECAP The electrostatic energy stored in the capacitor

Capacity increases if the dielectric material is introduced. If the battery is connected If the capacitor is charged, disconnected from battery, and then dielectric is introduced

Capacities with the dielectric Parallel plate capacitor Spherical capacitor Cylindrical capacitor

Electrostatic pressure Force on a plate of capacitor

Today’s plan Energy stored before and after the dielectric is filled. Force on a dielectric

Energy stored before and after Before  Since C = kC 0 Why U´< U ?? Where does this energy go?

Reason Dielectric, when inserted, gets pulled into the device. External agent do negative work to prevent the dielectric from accelerating. Work = U-U

The nonuniform electric field (fringing field) near the edges causes a dielectric to be pulled into the capacitor.

Fringing Field The bound charges tend to accumulate near the free charges of opposite sign.

If no external agent works, slab will be accelerated

Slab oscillates between the ends

Slab oscillates between the ends

Slab oscillates between the ends

Slab oscillates between the ends

To calculate the force due to electric field on the dielectric material

Let the external agent pulls the dielectric out by a infinitesimal displacement dx F ext dW = F ext dx F ext = dW/dx Electric force on the dielectric = -F ext x Plate area is L x L

Charge on the plates is constant

If the battery maintains a constant potential The force simply depends only upon the fringing field and free and bound charges

Two coaxial metal tubes stand vertically in a tank of dielectric oil (susceptibility e e and mass density .. Tubes are maintained at a potential difference of V. To what height (h) does the oil rise in the space between the tubes. Problem Griffiths Problem 4.28, page 196 vol 3.

Calculate the electrostatic energy stored between the plates of the cylindrical capacitor using the relation

r: a to b  : 0 to 2  Z: 0 to L

Problem 4.21 Griffiths A certain coaxial cable consists of a copper wire, radius a, surrounded by a concentric copper tube of inner radius c. The space between is partially filled (from b out to c) with a material of dielectric constant k e. Find the capacitance per unit length of this cable. a b c

Find the capacitance per unit length of this cable a b c Dielectric Material

a b c

A parallel plate capacitor is filled with a dielectric of dielectric constant k e. The k e varies parallel to an edge as Where x is the distance from the left end. Calculate the capacitance.

Find the C eq A B Twelve capacitors, each have capacity C are connected to form a cube.

A B E F

A B E F Q/3 Q/6 Q/3 Isolated system Total charge zero

A B E F Q/3 Q/6 Q/3