Two homogeneous dielectric regions 1 (p < 4 cm) and 2 (p 4 cm) have dielectric constants 3.5 and 1.5, respectively. If Dą = 12a, – 6as + 9a, nC/m², calculate (a) E and D1, (b) P2 and pv2s (c) the energy density for each region.
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- Consider a cylindrical capacitor with two layers of dielectric materials. The inner conductor radius is a and the outer conductor radius is c. The inner dielectric material fills the thickness (b-a) and its permittivity is & and the outer dielectric material fills the thickness (c-b) and its permittivity is ε, as shown in the figure. Find the capacitance of the capacitor if its length is 1. Consider a spherical capacitor with two layers of dielectric materials. The inner conductor radius is a and the outer conductor radius is c. The inner dielectric material fills the thickness (b-a) and its permittivity is & and the outer dielectric material fills the thickness (c-b) and its permittivity is ६, Find the capacitance of the capacitor.A dielectric-filled parallel-plate capacitor has plate area A = 10.0 cm2cm2 , plate separation d = 5.00 mmmm and dielectric constant k = 4.00. The capacitor is connected to a battery that creates a constant voltage V = 15.0 VV . Throughout the problem, use ϵ0 = 8.85×10−12 C2/N⋅m2C2/N⋅m2 . The dielectric plate is now slowly pulled out of the capacitor, which remains connected to the battery. Find the energy U2 of the capacitor at the moment when the capacitor is half-filled with the dielectric. The capacitor is now disconnected from the battery, and the dielectric plate is slowly removed the rest of the way out of the capacitor. Find the new energy of the capacitor, U3. In the process of removing the remaining portion of the dielectric from the disconnected capacitor, how much work is done by the external agent acting on the dielectric?a parallel-plate capacitor of plate area A = 11.5 cm2 and plate separation 2d= 7.40 mm. The left half of the gap is filled with material of dielectric constant κ1 = 22.8; the top of the right half is filled with material of dielectric constant κ2 = 41.3; the bottom of the right half is filled with material of dielectric constant κ3 = 60.4. What is the capacitance?
- A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius R₂ = 7.5 mm, and the outer one a radius R = 14 mm. The region between the cylinders contains a dielectric with constant =3.6. The common length of the cylinders is L=7.5 m (Assume the cylinders can be treated as ideal infinite cylinders.) Determine the potential energy stored in this capacitor when a potential difference V = 38.8V is applied between the inner and outer cylinders in n.J. ME hpA 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 ItSix Q.4: Eour capacitors are arranged in the following configuration: the capacitances of capacitors are C1= 1.5µF, C2= 3.5µF, C3= 2.0µF, C4= 2.5µF, Cs= 3.0µF and C6=4.0µF. The voltage V of the battery is 12.0V. (a) Calculate the capacitance of the configuration. (b) How much energy is stored in the configuration? (c) How much energy is stored in capacitor C1? C2 C3 C1