R Figure P25.5

In Lab 3, we measured the dielectric constant of glass using a parallel plate capacitor. Suppose that a piece of flat glass panel with a linear dielectric constant ɛ, = 2.5 is inserted between the plates of such a capacitor. The thickness of the glass is d = 5mm. The glass is in contact with both plates. One of the plates of the capacitor is kept at +3V, and the other plate is grounded. Treat the plates as infinitely large and thus the electric field is uniform between the plates. a) Calculate the electric field between the plates. b) Calculate the (uniform) polarization created in the glass. c) Calculate the surface bound charge density on the side of the glass that is in contact with the positive plate of the capacitor. d) Calculate the electric displacement between the plates. e) Calculate the free charge per unit area on the positive plate of the capacitor.

A system of very long conductors (Total length l) consists of an inner cylinder of radius a and a thin outer cylinder of radius b. The inner cylinder is given a total charge q while the outer cylinder has the same amount of charge but with the opposite sign. All charges are evenly distributed on the surface of the conductor. Determine: *The total capacitance and capacitance per unit length of this system!

A Geiger-Mueller tube is a radiation detector that consists of a closed, hollow, metal cylinder (the cathode) of inner radius ra and a coaxial cylindrical wire (the anode) of radius (see figure below) with a gas filling the space between the electrodes. Assume that the internal diameter of a Geiger-Mueller tube is 1.95 cm and that the wire along the axis has a diameter of 0.190 mm. The dielectric strength of the gas between the central wire and the cylinder is 1.25 x 106 V/m. Use the equation ain 2πrle= to calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas. €0 Anode Cathode 148 X Your response differs from the correct answer by more than 10%. Double check your calculations. V Need Help? Read It

9d K1=5 5d 8d 15d 15d 2d » K2=2 Two dielectric slabs with dielectric constants, K, and K2 are placed in parallel plate capacitor as shown in fig. Plates of the capacitor and both slabs have the same width of 15d. If the capacitance of the capacitor before slabs are inserted is Co, What is the capacitance of capacitor with slabs in terms of Co ?

1.

A Geiger-Mueller tube is a radiation detector that consists of a closed, hollow, metal cylinder (the cathode) of inner radius ra and a coaxial cylindrical wire (the anode) of radius (see figure below) with a gas filling the space between the electrodes. Assume that the internal diameter of a Geiger-Mueller tube is 1.85 cm and that the wire along the axis has a diameter of 0.195 mm. The dielectric strength of the gas between the central wire and the cylinder is 1.10 x 106 V/m. Use the equation 2 rlE = in to calculate the €0 maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas. Cathode Anode Ⓡ

A solid cylindrical conductor of radius 2.1 cm is coaxial with a cylindrical shell of negligible thickness, radius 2.3 cm. Find the capacitance ( in units of nF) of this cylindrical capacitor if its length is 36.6 m.

Note: The value of a=0, b=5 and C=7.