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Condition |
free/or 0.5$ |
| 801 | The space between two conducting concentric spheres of radii a and b (a < b) is filled up with homogeneous poorly conducting medium. The capacitance of such a system equals C. Find the resistivity of the medium if the potential difference between the spheres, when they are disconnected from an external voltage, decreases η-fold during the time interval Δt. |
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| 802 | Two metal balls of the same radius a are located in a homogeneous poorly conducting medium with resistivity ρ. Find the resistance of the medium between the balls provided that the separation between them is much greater than the radius of the ball. |
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| 803 | A metal ball of radius a is located at a distance l from an infinite ideally conducting plane. The space around the ball is filled with a homogeneous poorly conducting medium with resistivity ρ. In the case of a << l find: (a) the current density at the conducting plane as a function of distance r from the ball if the potential difference between the ball and the plane is equal to V; (b) the electric resistance of the medium between the ball and the plane. |
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| 804 | Two long parallel wires are located in a poorly conducting medium with resistivity ρ. The distance between the axes of the wires is equal to l, the cross-section radius of each wire equals a. In the case a << l find: (a) the current density at the point equally removed from the axes of the wires by a distance r if the potential difference between the wires is equal to V; (b) the electric resistance of the medium per unit length of the wires. |
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| 805 | The gap between the plates of a parallel-plate capacitor is filled with glass of resistivity ρ = 100 GΩ*m. The capacitance of the capacitor equals C = 4.0 nF. Find the leakage current of the capacitor when a voltage V = 2.0 kV is applied to it. |
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| 806 | Two conductors of arbitrary shape are embedded into an infinite homogeneous poorly conducting medium with resistivity ρ and permittivity ε. Find the value of a product RC for this system, where R is the resistance of the medium between the conductors, and C is the mutual capacitance of the wires in the presence of the medium. |
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| 807 | A conductor with resistivity p bounds on a dielectric with permittivity a. At a certain point A at the conductor's surface the electric displacement equals D, the vector D being directed away from the conductor and forming an angle a with the normal of the surface. Find the surface density of charges on the conductor at the point A and the current density in the conductor in the vicinity of the same point. |
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| 808 | The gap between the plates of a parallel-plate capacitor is filled up with an inhomogeneous poorly conducting medium whose conductivity varies linearly in the direction perpendicular to the plates from σ1 = 1.0 pS/m to σ2 = 2.0 pS/m. Each plate has an area S = 230 cm2, and the separation between the plates is d = 2.0 mm. Find the current flowing through the capacitor due to a voltage V = 300 V. |
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| 809 | Demonstrate that the law of refraction of direct current lines at the boundary between two conducting media has the form tan α2/tan α1 = σ2/σ1, where σ1 and σ2 are the conductivities of the media, α2 and α1 are the angles between the current lines and the normal of the boundary surface. |
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| 810 | Two cylindrical conductors with equal cross-sections and different resistivities ρ1 and ρ2 are put end to end. Find the charge at the boundary of the conductors if a current I flows from conductor 1 to conductor 2. |
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| 811 | The gap between the plates of a parallel-plate capacitor is filled up with two dielectric layers 1 and 2 with thicknesses d1 and d2, permittivities e1, and e2, and resistivities r1 and r2. A de voltage V is applied to the capacitor, with electric field directed from layer 1 to layer 2. Find a, the surface density of extraneous charges at the boundary between the dielectric layers, and the condition under which s = 0. |
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| 812 | An inhomogeneous poorly conducting medium fills up the space between plates 1 and 2 of a parallel-plate capacitor. Its permittivity and resistivity vary from values ε1, ρ1 at plate 1 to values ε2, ρ2 at plate 2. A dc voltage is applied to the capacitor through which a steady current I flows from plate 1 to plate 2. Find the total extraneous charge in the given medium. |
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| 813 | The space between the plates of a parallel-plate capacitor is filled up with inhomogeneous poorly conducting medium whose resistivity varies linearly in the direction perpendicular to the plates. The ratio of the maximum value of resistivity to the minimum one is equal to η. The gap width equals d. Find the volume density of the charge in the gap if a voltage V is applied to the capacitor. ε is assumed to be 1 everywhere. |
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| 814 | A long round conductor of cross-sectional area S is made of material whose resistivity depends only on a distance r from the axis of the conductor as ρ = α/r2, where α is a constant. Find: (a) the resistance per unit length of such a conductor; (b) the electric field strength in the conductor due to which a current I flows through it. |
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| 815 | A capacitor with capacitance C = 400 pF is connected via a resistance R = 650 S to a source of constant voltage V0. How soon will the voltage developed across the capacitor reach a value V = 0.90 V0? |
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| 816 | A capacitor filled with dielectric of permittivity ε = 2.1 loses half the charge acquired during a time interval τ = 3.0 min. Assuming the charge to leak only through the dielectric filler, calculate its resistivity. |
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| 817 | A circuit consists of a source of a constant emf ξ and a resist ance R and a capacitor with capacitance C connected in series. The internal resistance of the source is negligible. At a moment t = 0 the capacitance of the capacitor is abruptly decreased η-fold. Find the current flowing through the circuit as a function of time t. |
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| 818 | An ammeter and a voltmeter are connected in series to a battery with an emf ξ = 6.0 V. When a certain resistance is connected in parallel with the voltmeter, the readings of the latter decrease η = 2.0 times, whereas the readings of the ammeter increase the same number of times. Find the voltmeter readings after the connection of the resistance. |
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| 819 | Find a potential difference f1 — f2 between points 1 and 2 of the circuit shown in Fig. 3.39 if R1= 10 S, R2 = 20 S, e1=5.0 V, and e2 = 2.0 V. The internal resistances of the current sources are negligible. |
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| 820 | Two sources of current of equal emf are connected in series and have different internal resistances R1 and R2. (R2>R1). Find the external resistance R at which the potential difference across the terminals of one of the sources (which one in particular?) becomes equal to zero. |
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