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Condition |
free/or 0.5$ |
| 941 | A copper connector of mass m slides down two smooth copper bars, set at an angle α to the horizontal, due to gravity (Fig. 3.84). At the top the bars are interconnected through a resistance R. The separation between the bars is equal to l. The system is located in a uniform magnetic field of induction B, perpendicular to the plane in which the connector slides. The resistances of the bars, the connector and the sliding contacts, as well as the self-inductance of the loop, are assumed to be negligible. Find the steady-state velocity of the connector. |
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| 942 | The system differs from the one examined in the foregoing problem (Fig. 3.84) by a capacitor of capacitance C replacing the resistance R. Find the acceleration of the connector. |
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| 943 | A wire shaped as a semi-circle of radius a rotates about an axis OO' with an angular velocity co in a uniform magnetic field of induction B (Fig. 3.85). The rotation axis is perpendicular to the field direction. The total resistance of the circuit is equal to R. Neglecting the magnetic field of the induced current, find the mean amount of thermal power being generated in the loop during a rotation period. |
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| 944 | A small coil is introduced between the poles of an electromagnet so that its axis coincides with the magnetic field direction. The cross-sectional area of the coil is equal to S = 3.0 mm2, the number of turns is N = 60. When the coil turns through 180° about its diameter, a ballistic galvanometer connected to the coil indicates a charge q = 4.5 mC flowing through it. Find the magnetic induction magnitude between the poles provided the total resistance of the electric circuit equals R = 40 S. |
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| 945 | A square wire frame with side a and a straight conductor carrying a constant current I are located in the same plane (Fig. 3.86). The inductance and the resistance of the frame are equal to L and R respectively. The frame was turned through 180° about the axis OO' separated from the current-carrying conductor by a distance b. Find the electric charge having flown through the frame. |
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| 946 | A long straight wire carries a current I0. At distances a and b from it there are two other wires, parallel to the former one, which are interconnected by a resistance R (Fig. 3.87). A connector slides without friction along the wires with a constant velocity v. Assuming the resistances of the wires, the connector, the sliding contacts, and the self-inductance of the frame to be negligible, find: (a) the magnitude and the direction of the current induced in the connector; (b) the force required to maintain the connector's velocity constant. |
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| 947 | A conducting rod AB of mass m slides without friction over two long conducting rails separated by a distance l (Fig. 3.88). At the left end the rails are interconnected by a resistance R. The system is located in a uniform magnetic field perpendicular to the plane of the loop. At the moment t = 0 the rod AB starts moving to the right with an initial velocity v0. Neglecting the resistances of the rails and the rod AB, as well as the self-inductance, find: (a) the distance covered by the rod until it comes to a standstill; (b) the amount of heat generated in the resistance R during this process. |
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| 948 | A connector AB can slide without friction along a Π-shaped conductor located in a horizontal plane (Fig. 3.89). The connector has a length l, mass m, and resistance R. The whole system is located in a uniform magnetic field of induction B directed vertically. At the moment t = 0 a constant horizontal force F starts acting on the connector shifting it translationwise to the right. Find how the velocity of the connector varies with time t. The inductance of the loop and the resistance of the Π-shaped conductor are assumed to be negligible. |
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| 949 | Fig. 3.90 illustrates plane figures made of thin conductors which are located in a uniform magnetic field directed away from a reader beyond the plane of the drawing. The magnetic induction starts diminishing. Find how the currents induced in these loops are directed. |
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| 950 | A plane loop shown in Fig. 3.91 is shaped as two squares with sides a = 20 cm and b = 10 cm and is introduced into a uniform magnetic field at right angles to the loop's plane. The magnetic induction varies with time as B = B0 sin ωt, where B0 = 10 mT and ω = 100 s-1 . Find the amplitude of the current induced in the loop if its resistance per unit length is equal to ρ = 50 mΩ/m. The inductance of the loop is to be neglected. |
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| 951 | A plane spiral with a great number N of turns wound tightly to one another is located in a uniform magnetic field perpendicular to the spiral's plane. The outside Fig. 3.91. radius of the spiral's turns is equal to a. The magnetic induction varies with time as B = B0sinwt, where B0 and co are constants. Find the amplitude of emf induced in the spiral. |
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| 952 | A Π-shaped conductor is located in a uniform magnetic field perpendicular to the plane of the conductor and varying with time at the rate B' = 0.10 T/s. A conducting connector starts moving with an acceleration w = 10 cm/s2 along the parallel bars of the conductor. The length of the connector is equal to l = 20 cm. Find the emf induced in the loop t = 2.0 s after the beginning of the motion, if at the moment t = 0 the loop area and the magnetic induction are equal to zero. The inductance of the loop is to be neglected. |
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| 953 | In a long straight solenoid with cross-sectional radius a and number of turns per unit length n a current varies with a constant velocity I' A/s. Find the magnitude of the eddy current field strength as a function of the distance r from the solenoid axis. Draw the approximate plot of this function. |
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| 954 | A long straight solenoid of cross-sectional diameter d = 5 cm and with n = 20 turns per one cm of its length has a round turn of copper wire of cross-sectional area S = 1.0 mm2 tightly put on its winding. Find the current flowing in the turn if the current in the solenoid winding is increased with a constant velocity I' = 100 A/s. The inductance of the turn is to be neglected. |
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| 955 | A long solenoid of cross-sectional radius a has a thin insulated wire ring tightly put on its winding; one half of the ring has the resistance η times that of the other half. The magnetic induction produced by the solenoid varies with time as B = bt, where b is a constant. Find the magnitude of the electric field strength in the ring. |
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| 956 | A thin non-conducting ring of mass m carrying a charge q can freely rotate about its axis. At the initial moment the ring was at rest and no magnetic field was present. Then a practically uniform magnetic field was switched on, which was perpendicular to the plane of the ring and increased with time according to a certain law B(t). Find the angular velocity ω of the ring as a function of the induction B(t). |
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| 957 | A thin wire ring of radius a and resistance r is located inside a long solenoid so that their axes coincide. The length of the solenoid is equal to L, its cross-sectional radius, to b. At a certain moment the solenoid was connected to a source of a constant voltage V. The total resistance of the circuit is equal to R. Assuming the inductance of the ring to be negligible, find the maximum value of the radial force acting per unit length of the ring. |
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| 958 | A magnetic flux through a stationary loop with a resistance R varies during the time interval τ as Φ = at(τ - t). Find the amount of heat generated in the loop during that time. The inductance of the loop is to be neglected. |
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| 959 | In the middle of a long solenoid there is a coaxial ring of square cross-section, made of conducting material with resistivity p. The thickness of the ring is equal to h, its inside and outside radii are equal to a and b respectively. Find the current induced in the ring if the magnetic induction produced by the solenoid varies with time as B = bt, where b is a constant. The inductance of the ring is to be neglected. |
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| 960 | How many metres of a thin wire are required to manufacture a solenoid of length L0 = 100 cm and inductance L = 1.0 mH if the solenoid's cross-sectional diameter is considerably less than its length? |
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