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Condition |
free/or 0.5$ |
| 861 | A parallel-plate air capacitor whose plates are separated by a distance d = 5.0 mm is first - charged to a potential difference V = 90 V and then disconnected from a de voltage source. Find the time interval during which the voltage across the capacitor decreases by n = 1.0%, taking into account that the average number of ion pairs formed in air under standard conditions per unit volume per unit time is equal to n i = 5.0 cm-3 •s -1 and that the given volt-age corresponds to the saturation current. |
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| 862 | The gap between two plane plates of a capacitor equal to d is filled with a gas. One of the plates emits v o electrons per second which, moving in an electric field, ionize gas molecules; this way each electron produces a new electrons (and ions) along a unit length of its path. Find the electronic current at the opposite plate, neglecting the ionization of gas molecules by formed ions. |
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| 863 | The gas between the capacitor plates separated by a distance d is uniformly ionized by ultraviolet radiation so that n i electrons per unit volume per second are formed. These electrons moving in the electric field of the capacitor ionize gas molecules, each electron producing cc new electrons (and ions) per unit length of its path. Neglecting the ionization by ions, find the electronic current density at the plate possessing a higher potential. |
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| 864 | A current I = 1.00 A circulates in a round thin-wire loop of radius R = 100 mm. Find the magnetic induction (a) at the centre of the loop; (b) at the point lying on the axis of the loop at a distance x = 100 mm from its centre. |
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| 865 | A current I flows along a thin wire shaped as a regular polygon with n sides which can be inscribed into a circle of radius R. Find the magnetic induction at the centre of the polygon. Analyse the obtained expression at n → ∞. |
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| 866 | Find the magnetic induction at the centre of a rectangular wire frame whose diagonal is equal to d = 16 cm and the angle between the diagonals is equal to φ = 30°; the current flowing in the frame equals I = 5.0 A. |
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| 867 | A current I = 5.0 A flows along a thin wire shaped as shown in Fig. 3.59. The radius of a curved part of the wire is equal to R = 120 mm, the angle 2φ = 90°. Find the magnetic induction of the field at the point O. |
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| 868 | Find the magnetic induction of the field at the point O of a loop with current I, whose shape is illustrated (a) in Fig. 3.60a, the radii a and b, as well as the angle φ are known; (b) in Fig. 3.60b, the radius a and the side b are known. |
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| 869 | A current I flows along a lengthy thin-walled tube of radius R with longitudinal slit of width h. Find the induction of the magnetic field inside the tube under the condition h << R. |
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| 870 | A current I flows in a long straight wire with cross-section having the form of a thin half-ring of radius R (Fig. 3.61). Find the induction of the magnetic field at the point O. |
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| 871 | Find the magnetic induction of the field at the point O if a current-carrying wire has the shape shown in Fig. 3.62 a, b, c. The radius of the curved part of the wire is R, the linear parts are assumed to be very long. |
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| 872 | A very long wire carrying a current I = 5.0 A is bent at right angles. Find the magnetic induction at a point lying on a perpendicular to the wire, drawn through the point of bending, at a distance l = 35 cm from it. |
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| 873 | Find the magnetic induction at the point O if the wire carrying a current I = 8.0 A has the shape shown in Fig. 3.63 a, b, c. The radius of the curved part of the wire is R = 100 mm, the linear parts of the wire are very long. |
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| 874 | Find the magnitude and direction of the magnetic induction vector B (a) of an infinite plane carrying a current of linear density i; the vector i is the same at all points of the plane; (b) of two parallel infinite planes carrying currents of linear densities i and -i; the vectors i and -i are constant at all points of the corresponding planes. |
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| 875 | A uniform current of density j flows inside an infinite plate of thickness 2d parallel to its surface. Find the magnetic induction induced by this current as a function of the distance x from the median plane of the plate. The magnetic permeability is assumed to be equal to unity both inside and outside the plate. |
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| 876 | A direct current I flows along a lengthy straight wire. From the point O (Fig. 3.64) the current spreads radially all over an infinite conducting plane perpendicular to the wire. Find the magnetic induction at all points of space. |
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| 877 | A current I flows along a round loop. Find the integral ∫ B dr along the axis of the loop within the range from -∞ to +∞. Explain the result obtained. |
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| 878 | A direct current of density j flows along a round uniform straight wire with cross-section radius R. Find the magnetic induction vector of this current at the point whose position relative to the axis of the wire is defined by a radius vector r. The magnetic permeability is assumed to be equal to unity throughout all the space. |
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| 879 | Inside a long straight uniform wire of round cross-section there is a long round cylindrical cavity whose axis is parallel to the axis of the wire and displaced from the latter by a distance l. A direct current of density j flows along the wire. Find the magnetic induction inside the cavity. Consider, in particular, the case l = 0. |
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| 880 | Find the current density as a function of distance r from the axis of a radially symmetrical parallel stream of electrons if the magnetic induction inside the stream varies as B = brα, where b and α are positive constants. |
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