C4_1. A speck of dust with a massand charge, flies into electric field vertical high capacitor at a point located in the middle between its plates (see figure, top view).

What should be the minimum speed with which a dust particle flies into the capacitor so that it can fly through it? The length of the capacitor plates is 10 cm, the distance between the plates is 1 cm, the voltage across the capacitor plates is 5,000 V. The system is in a vacuum.

C 4_2. Small ball with chargeand weighing 3 g, suspended on a weightless thread with an elasticity coefficient of 100 N/m, is located between the vertical plates of a flat air capacitor. The distance between the capacitor plates is 5 cm. What is the potential difference between the capacitor plates if the filament lengthening is 0.5 mm?

C 4_3. parallel to the plates (see figure), the distance between whichd .

At what angle will the electron velocity vector deviate from the initial direction when leaving the capacitor, if the capacitor is charged to a potential difference? Insert length. Neglect the effect of gravity on the electron.

C 4_4. An electron flies into a flat capacitor with a speedparallel to the plates (see figure, top view), the distance between whichd .

What is the potential difference between the plates of the capacitor, if, when flying out of the capacitor, the electron velocity vector deviates from the original direction by an angle? Insert length.

C 4_5. Hollow ball masswith chargemoves in a uniform horizontal electric field from rest. The trajectory of the ball forms an angle with the vertical. What is the modulus of tension electric field E ?

C 4_6. A hollow charged ball of massmoves in a uniform horizontal electric field from rest. Electric field strength modulus. The trajectory of the ball forms an angle with the vertical. What is the charge of the ballq ?

C 4_7. An electron flies into the space between two oppositely charged plates of a flat capacitor with a speedv o ( v o << с) параллельно пластинам (см. рисунок). Расстояние между пластинами d, длина пластин L (L >> d), potential difference between the plates Δφ. Determine the tangent of the angle by which the electron will deviate after leaving the capacitor.

C 4_8. Two point chargesAnd, located at a distancefrom each other, attract with force. The sum of the charges is. What are the moduli of these charges? Round your answer to the nearest tenth of a microcoulomb.

C 4_9.

C 4 No. 3689. Two identical air condenser connected in series and connected to the source constant voltage. Then one of them, without breaking the chain, was lowered into oil with permittivity . How and how many times will the energy of the second capacitor, which remained not immersed in oil, change in this case?C 4 No. 3689. Two identical air capacitors are connected in series and connected to a constant voltage source. Then one of them, without breaking the circuit, was lowered into oil with a permittivity. How and how many times will the energy of the second capacitor, which remained not immersed in oil, change in this case?

C 4 No. 4218. Inside an uncharged metal sphere of radius r 1 = 40 cm there are two spherical cavities with radiilocated in such a way that their surfaces almost touch in the center of the ball. A charge is placed in the center of one cavitynC, and then in the center another - chargenC (see figure). Find the modulus and direction of the stress vectorelectrostatic field at a pointlocated at a distance= 1 m from the center of the ball on the perpendicular to the segment connecting the centers of the cavities.

Solution.

Possible Solution

In electrostatics, it is considered that there is no electric field inside the metal, since otherwise the free charges inside the metal would move. Therefore, when placing a chargecharge is induced in the first cavity on its wallsand according to the principle of superposition, the total field of these two charges in the metal of the ball is equal to zero. According to the law of conservation of electric charge and due to the electroneutrality of the ball, the excess charge is equal to. It is displaced to the surface of the ball and evenly distributed over it, since the charges inside the metal do not create a field and do not affect the distribution of charges on the surface of the ball.

№ 1 An electron flying horizontally with a speed = 1500 km/s flew into a uniform electric field with intensity E= 100 V/cm directed vertically upwards. What will be the magnitude and direction of the electron's velocity through t= 10 -9 s?

№ 2 Two identical flat air capacitors are connected in series and connected to a source of electric current with constant EMF. Inside one of them, a dielectric with a permittivity =4 is introduced. The dielectric fills the entire space between the plates of the capacitor. How and how many times will the electric field strength in this capacitor change?

№ 3 On the plates of a flat air capacitor with a plate area S \u003d 150 cm 2 is a charge q = 510 -8 Cl. What is the force of mutual attraction between the plates and the volume energy density of the capacitor field?

№ 4 During the time τ = 10 C with a uniformly increasing current strength from zero to a certain maximum in a conductor with resistance R\u003d 25 Ohm the amount of heat released Q= 40 kJ. Determine the average current<I> in the explorer.

№ 5 In the conductor for the time τ = 10 s with a uniform increase in current strength from I 1 = 1.5 A up to I 2 \u003d 3 A amount of heat released Q= 15 kJ. Find resistance R conductor.

№ 6 In a copper conductor of length l = 1.5 m and cross-sectional area S\u003d 0.4 mm 2 current flows. In this case, the amount of heat is released every second Q\u003d 0.35 J. How many electrons pass in 1 s through the cross section of this conductor?

№ 7 Inside the long solenoid, perpendicular to its axis, there is a conductor of length l\u003d 5 cm, through which the current passes I 1 \u003d 10 A. What force acts on the conductor if the solenoid has n\u003d 25 turns per centimeter of length and a current flows through its winding with a force I 2 \u003d 5 A?

№ 8 In a uniform magnetic field with induction B \u003d 0.1 T, a flat wire coil is located, the area of ​​\u200b\u200bwhich S \u003d 10 3 cm 2, and the resistance R \u003d 2 Ohm, so that its plane makes an angle  = 40 with induction lines. The coil is closed to the galvanometer. At what angle was the coil turned if the total charge flowing through the galvanometer when the coil was turned q\u003d 7.510 -5 Cl.

№ 9 The current source is closed to the coil with resistance R= 58 Ohm. Through time t= 0.1 s the current in the coil has reached 96% of the maximum value. Determine the inductance of the coil.

№ 10 The oscillatory circuit consists of a flat capacitor and an inductor L= 5 mH. Distance between capacitor plates d= 3 mm, plate area S\u003d 2.5 cm 2 each, dielectric - mica ( 1 \u003d 6.0). By how many hertz will the oscillation frequency in the circuit change if we replace the dielectric in the capacitor with paraffin ( 2 = 2.0)?

Option 8

№ 1 Three identical point charges q 1 =q 2 =q 3 \u003d 2 nC are located at the vertices of an equilateral triangle with sides a\u003d 10 cm. Determine the module and direction of the force acting on one of the charges from the other two.

№ 2 Two capacitance capacitors WITH 1 = 3 uF and WITH 2 = 5 uF connected in series and connected to a DC voltage source U = 12 V. Determine the charge of each capacitor and the potential difference between its plates

№ 3 Find the force of attraction F between the plates of a flat capacitor, if the area of ​​each plate S \u003d 100 cm 2, the distance between them d = 3 mm, permittivity of the medium between the plates ε = 3.5. The capacitor is connected to a constant voltage source U = 250 V.

№ 4 Two sources with different EMF ( 1 \u003d 1.0 V,  2 \u003d 2 V) and internal resistances (r 1 = 0.5 ohm and r 2 = 0.1 ohm) connected in parallel with external resistance R. Determine the value of this resistance if the ammeter included in the circuit of the first element shows 1.5 A. Ammeter resistance R A= 0.05 ohm.

№ 5 By conductor resistance R\u003d 10 ohms, a uniformly increasing current flows. During τ = 8 s the amount of heat released in the conductor Q= 2500 J. Find the charge q, passing in the conductor during this time, if the current strength at the initial moment of time I 0 =0.

№ 6 Between the plates of a flat capacitor with an area S\u003d 250 cm 2 each is V=0.5 l of hydrogen. Ion concentration in gas n\u003d 5.310 7 cm -3. What voltage U must be applied to the plates of a capacitor in order to obtain a current with a force I\u003d 2.5 μA? Mobility of positive hydrogen ions b+ \u003d 5.410 -4 m 2 / Vs, negative b- \u003d 7.410 -4 m 2 / Vs.

№ 7 How should a straight aluminum conductor be placed in a uniform magnetic field with induction IN\u003d 0.04 T and what strength of current to pass through it so that it is in balance. Conductor radius R = 1 mm.

№ 8 Square frame of copper wire S\u003d 25 cm 2 is placed in a magnetic field with induction B\u003d 0.1 T. The frame plane is perpendicular to the field lines. How much electricity will pass through the contour of the frame when the magnetic field disappears? Cross-sectional area of ​​copper wire S 0 \u003d 1 mm 2.

№ 9 IN electrical circuit containing an inductance coil L= 2.5 H and a current source. Without breaking the circuit, the current source was turned off. Through time t= 5 ms the current in the coil will decrease to 0.001 of the original value. Determine the resistance of the coil.

№ 10 Capacitor WITH= 500 pF connected in parallel with a coil of length l= 30 cm and cross section S\u003d 4.5 cm 2 containing N= 1000 turns. The core is non-magnetic. Find frequency  contour oscillations.

18.20 . Two capacitors, rated for a maximum voltage of 300 V each, but having different capacitances of 500 and 300 pF, are connected in series. What is the maximum voltage that can be applied to such a compound capacitor?

18.21 . Three capacitors with capacitances of 1, 2 and 3 uF are connected in series and connected to a voltage source with an EMF of 220 V. Determine the charge of each capacitor (in µC).

18.22 . Two identical flat air capacitors are connected in series and connected to a voltage source. When one of the capacitors was immersed in a liquid dielectric, the charges on the capacitor plates increased 1.5 times. Find the permittivity of the dielectric.

18.23 . Inside a flat capacitor, parallel to its plates, a dielectric plate is placed, the area of ​​\u200b\u200bwhich is equal to the area of ​​​​the plates, and the thickness is half the distance between them. By what percentage will the capacitance of the capacitor increase if the permittivity of the plate is 4?

18.24 . What should be the capacitance (in pF) of the capacitor that must be connected in series with the 800 pF capacitor to make a 160 pF capacitor bank?

18.25 . A flat capacitor with a capacity of 20 pF is connected in series with the same capacitor, but filled with a dielectric with a permittivity of 3. Find the capacitance (in pF) of such a battery.

18.26 . An air flat capacitor with a capacity of 5 μF is filled with a liquid dielectric with a permittivity of 6. What capacitor (in μF) must be connected in series with the given one so that such a battery again has a capacity of 5 μF?

18.27 . Two capacitors, the capacitances of which are 2 and 4 microfarads, are connected in series and connected to a voltage source with an EMF of 75 V. Find the potential difference across the larger capacitor.

18.28 . Two identical flat air capacitors are connected in series and connected to a voltage source. A dielectric (ε = 3) is introduced inside one of them, filling the entire space between the plates. How many times will the field strength decrease in this capacitor?

18.29 . Two identical air capacitors are connected in series and connected to a constant voltage source. In one of them, the distance between the plates is tripled. How many times will the field strength decrease in this capacitor?

18.30 . Two identical air capacitors are connected in series and connected to a constant voltage source. In one of them, the distance between the plates is reduced by a factor of three, and in the other, the distance between the plates is tripled. How many times will the voltage on the second capacitor decrease?

18.31 . A flat capacitor with a capacity of 5 pF with a distance between the plates of 2 mm is connected to a voltage source with an EMF of 2 V. A flat metal plate 1 mm thick is inserted parallel to them into the space between the plates so that it completely covers the cavity inside the capacitor. Determine the amount of charge (in pC) that will pass through the source when the plate is inserted.