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In a region where the permittivity is uniform and where there is no unpaired charge, the electric potential obeys Laplace's equation.
If all of the region of interest is filled by a uniform dielectric, it is clear from the foregoing that all equations developed for fields in free space are now valid in the presence of the uniform dielectric. The only alteration is the replacement of the permittivity of free space o by that of the uniform dielectric. where and E were determined in a region of free space bounded by equipotentials, that region could just as well be filled with a uniform dielectric, and for the same potentials, the electric field intensity would be unaltered. However, the surface charge density on the boundaries would then be increased by the ratio /o.
(1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two laye ers of dielectrics, di and de thick, with permittivities s and s2, respectively. Ignoring the r...
Problem 1. Electrostatics (1) As shown in the Figure below, a parallel-plate capacitor of plate area A is filled with two layers of dielectrics, ch and d2 thick, with permittivities fringe effect at the four edges (assuming rectangular plates), find the fields Ei and Es in the two dielectrics if a voltage V (assumed positive) is applied to the top plate with regard to the bottom plate. (Note: both magnitudes and directions needed.) and a, respectively. Ignoring the (2) Find...
3. Find the capacitance of a parallel plate capacitor filled with two dielectrics as shown. The area is A, the thickness is d, and each dielectric is half the total thickness, i.e., d/2. What would the answer be if the two dielectrics were arranged as shown in the second picture (each with A/2, but thickness d)? E1 2 E1 E기
(a) What plate area is required if an air-filled, parallel-plate capacitor with a plate separation of 2.9 mm is to have a capacitance of 28 pF? (b) What is the maximum voltage that can be applied to this capacitor without causing dielectric breakdown?
The plates of a parallel-plate capacitor each have an area of 0.1 m2 and are separated by a 1 mm thick layer of glass. The capacitor is connected to a 11 V battery. (The dielectric constant for glass is 5.) a) Find the capacitance. b) Find the charge stored. c) Find the electric field between the plates.
The figure shows a parallel-plate capacitor of plate area A and plate separation d. A potential differenceV0 is applied between the plates. While the battery remains connected, a dielectric slab of thickness b and dielectric constant κ is placed between the plates as shown. Assume A = 130 cm2, d = 1.94 cm, V0 = 72.6 V, b = 0.735 cm, and κ = 3.15. Calculate (a) the capacitance,(b) the charge on the capacitor plates,(c) the electric field in the gap, and(d)...
Two parallel plates, each having area A 3676cm are connected to the terminals of a battery of voltage V, 6 V A as shown. The plates are separated by a distance d 0.42cm. You may assume (contrary to the drawing) that the separation between the plates is small compared to a linear dimension of the plate + A 1) What is C, the capacitance of this parallel plate capacitor? 7.746E-4 uF Submit 2) What is Q, the charge stored on...
A parallel plate capacitor is made of plates of area 0.05 m? each. The plates are separated by a distance of 0.200 mm. Initially, the space between the plates is filled with air. (a) What is the capacitance of this air-filled capacitor? (b) If the electric field inside the capacitor exceeds 3.00 x 106 V/m, the air undergoes electrical break- down. (This maximum field is known as the dielectric strength of air.) From this, calculate the maxi- mum voltage (potential...
A parallel-plate capacitor of capacitance Co, plate area A, spacing d is charged to voltage V. and then disconnected from the charging battery. A slab with dielectric constant K and thickness d/2 is thrust into the capacitor, as shown in the figure below; the slab is exactly halfway between the plates. к (a) What is the new capacitance in terms of Co? (b) What is the ratio of the stored energy before to that after the slab is inserted (U/0.)?...
Problem 5 The space between the plates of a parallel-plate capacitor, shown below, is filled with two slabs of different dielectric materials. The slab at the top has thickness 2d and a relative dielectric constant of er1 = 3 and the one at the bottom has thickness d and a relative dielectric constant of er2 = 2. The capacitor plates have surface area S. a. Assume a total charge of +Q on the top plate and -Q on the bottom plate. Find...
Two parallel plates, each having area A- 2737cm are connected to the terminals of a battery of voltage Vb 6 V as shown. The plates are separated by a distance d 0.38cm. You may assume (contrary to the drawing) that the separation between the plates is small compared to a linear dimension of the plate 1) What is C, the capacitance of this parallel plate capacitor? Submit 2) What is Q, the charge stored on the top plate of the...