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free/or 0.5$ |
| 741 | A dielectric ball is polarized uniformly and statically. Its polarization equals P. Taking into account that a ball polarized in this way may be represented as a result of a small shift of all positive charges of the dielectric relative to all negative charges, (a) find the electric field strength E inside the ball; (b) demonstrate that the field outside the ball is that of a dipole located at the centre of the ball, the potential of that field being equal to φ = p0r/4πε0, where p0 is the electric moment of the ball, and r is the distance from its centre. |
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| 742 | Utilizing the solution of the foregoing problem, find the electric field strength E0 in a spherical cavity in an infinite statically polarized uniform dielectric if the dielectric's polarization is P, and far from the cavity the field strength is E. |
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| 743 | A uniform dielectric ball is placed in a uniform electric field of strength E0. Under these conditions the dielectric becomes polarized uniformly. Find the electric field strength E inside the ball and the polarization P of the dielectric whose permittivity equals e. Make use of the result obtained in Problem 3.96. |
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| 744 | An infinitely long round dielectric cylinder is polarized uniformly and statically, the polarization P being perpendicular to the axis of the cylinder. Find the electric field strength E inside the dielectric. |
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| 745 | A long round cylinder made of uniform dielectric is placed in a uniform electric field of strength E0. The axis of the cylinder is perpendicular to vector E0. Under these conditions the dielectric becomes polarized uniformly. Making use of the result obtained in the foregoing problem, find the electric field strength E in the cylinder and the polarization P of the dielectric whose permittivity is equal to e. |
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| 746 | Find the capacitance of an isolated ball-shaped conductor of radius R1 surrounded by an adjacent concentric layer of dielectric with permittivity ε and outside radius R2. |
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| 747 | Two parallel-plate air capacitors, each of capacitance C, were connected in series to a battery with emf ξ. Then one of the capacitors was filled up with uniform dielectric with permittivity ε. How many times did the electric field strength in that capacitor decrease? What amount of charge flows through the battery? |
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| 748 | The space between the plates of a parallel-plate capacitor is filled consecutively with two dielectric layers 1 and 2 having the thicknesses d1 and d2 and the permittivities ε1 and ε2 respectively. The area of each plate is equal to S. Find: (a) the capacitance of the capacitor; (b) the density σ' of the bound charges on the boundary plane if the voltage across the capacitor equals V and the electric field is directed from layer 1 to layer 2. |
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| 749 | The gap between the plates of a parallel-plate capacitor is filled with isotropic dielectric whose permittivity ε varies linearly from ε1 to ε2 (ε2 > ε1) in the direction perpendicular to the plates. The area of each plate equals S, the separation between the plates is equal to d. Find: (a) the capacitance of the capacitor; (b) the space density of the bound charges as a function of ε if the charge of the capacitor is q and the field E in it is directed toward the growing ε values. |
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| 750 | Find the capacitance of a spherical capacitor whose electrodes have radii R1 and R2 > R1 and which is filled with isotropic dielectric whose permittivity varies as ε = a/r, where a is a constant, and r is the distance from the centre of the capacitor. |
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| 751 | A cylindrical capacitor is filled with two cylindrical layers of dielectric with permittivities el and e2. The inside radii of the layers are equal to R1 and R2 > R1. The maximum permissible values of electric field strength are equal to E1m and E2m for these dielectrics. At what relationship between a, R, and En, will the voltage increase result in the field strength reaching the breakdown value for both dielectrics simultaneously? |
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| 752 | There is a double-layer cylindrical capacitor whose parameters are shown in Fig. 3.16. The breakdown field strength values for these dielectrics are equal to E1 and E2 respectively. What is the breakdown voltage of this capacitor if e1R1E1< e2R2E2? |
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| 753 | Two long straight wires with equal cross-sectional radii a are located parallel to each other in air. The distance between their axes equals b. Find the mutual capacitance of the wires per unit length under the condition b >> a. |
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| 754 | Along straight wire is located parallel to an infinite conducting plate. The wire cross-sectional radius is equal to a, the distance between the axis of the wire and the plane equals b. Find the mutual capacitance of this system per unit length of the wire under the condition a << b. |
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| 755 | Find the capacitance of a system of two identical metal balls of radius a if the distance between their centres is equal to b, with b >> a. The system is located in a uniform dielectric with permittivity ε. |
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| 756 | Determine the capacitance of a system consisting of a metal ball of radius a and an infinite conducting plane separated from the centre of the ball by the distance l if l >> a. |
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| 757 | Find the capacitance of a system of identical capacitors between points A and B shown in (a) Fig. 3.17a; (b) Fig. 3.17b. |
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| 758 | Four identical metal plates are located in air at equal distances d from one another. The area of each plate is equal to S. Find the capacitance of the system between points A and B if the plates are interconnected as shown (a) in Fig. 3.18a; (b) in Fig. 3.18b. |
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| 759 | A capacitor of capacitance C1 = 1.0 μF withstands the maximum voltage V1 = 6.0 kV while a capacitor of capacitance C2 = 2.0 μF, the maximum voltage V2 = 4.0 kV. What voltage will the system of these two capacitors withstand if they are connected in series? |
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| 760 | Find the potential difference between points A and B of the system shown in Fig. 3.19 if the emf is equal to ξ = 110 V and the capacitance ratio C2/C1 = η = 2.0. |
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