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Condition |
free/or 0.5$ |
| 901 | Two long parallel wires of negligible resistance are connected at one end to a resistance R and at the other end to a dc voltage source. The distance between the axes of the wires is η = 20 times greater than the cross-sectional radius of each wire. At what value of resistance R does the resultant force of interaction between the wires turn into zero? |
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| 902 | A direct current I flows in a long straight conductor whose cross-section has the form of a thin half-ring of radius R. The same current flows in the opposite direction along a thin conductor located on the "axis" of the first conductor (point O in Fig. 3.61). Find the magnetic interaction force between the given conductors reduced to a unit of their length. |
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| 903 | Two long thin parallel conductors of the shape shown in Fig. 3.71 carry direct currents I1 and I2. The separation between the conductors is a, the width of the right-hand conductor is equal to b. With both conductors lying in one plane, find the magnetic interaction force between them reduced to a unit of their length. |
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| 904 | A system consists of two parallel planes carrying currents producing a uniform magnetic field of induction B between the planes. Outside this space there is no magnetic field. Find the magnetic force acting per unit area of each plane. |
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| 905 | A conducting current-carrying plane is placed in an external uniform magnetic field. As a result, the magnetic induction becomes equal to B1 on one side of the plane and to B2, on the other. Find the magnetic force acting per unit area of the plane in the cases illustrated in Fig. 3.72. Determine the direction of the current in the plane in each case. |
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| 906 | In an electromagnetic pump designed for transferring molten metals a pipe section with metal is located in a uniform magnetic field of induction B (Fig. 3.73). A current I is made to flow across this pipe section in the direction perpendicular both to the vector B and to the axis of the pipe. Find the gauge pressure produced by the pump if B = 0.10 T, I = 100 A, and a = 2.0 cm. |
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| 907 | A current I flows in a long thinwalled cylinder of radius R. What pressure do the walls of the cylinder experience? |
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| 908 | What pressure does the lateral surface of a long straight solenoid with n turns per unit length experience when a current I flows through it? |
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| 909 | A current I flows in a long single-layer solenoid with cross-sectional radius R. The number of turns per unit length of the solenoid equals n. Find the limiting current at which the winding may rupture if the tensile strength of the wire is equal to Flim. |
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| 910 | A parallel-plate capacitor with area of each plate equal to S and the separation between them to d is put into a stream of conducting liquid with resistivity p. The liquid moves parallel to the plates with a constant velocity v. The whole system is located in a uniform magnetic field of induction B, vector B being parallel to the plates and perpendicular to the stream direction. The capacitor plates are interconnected by means of an external resistance R. What amount of power is generated in that resistance? At what value of R is the generated power the highest? What is this highest power equal to? |
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| 911 | A straight round copper conductor of radius R = 5.0 mm carries a current I = 50 A. Find the potential difference between the axis of the conductor and its surface. The concentration of the conduction electrons in copper is equal to n = 0.9·10^23 cm-3. |
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| 912 | In Hall effect measurements in a sodium conductor the strength of a transverse field was found to be equal to E = 5.0 μV/cm with a current density j = 200 A/cm2 and magnetic induction B = 1.00 T. Find the concentration of the conduction electrons and its ratio to the total number of atoms in the given conductor. |
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| 913 | Find the mobility of the conduction electrons in a copper conductor if in Hall effect measurements performed in the magnetic field of induction B = 100 mT the transverse electric field strength of the given conductor turned out to be η = 3.1*103 times less than that of the longitudinal electric field. |
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| 914 | A small current-carrying loop is located at a distance r from a long straight conductor with current I. The magnetic moment of the loop is equal to pm. Find the magnitude and direction of the force vector applied to the loop if the vector pm (a) is parallel to the straight conductor; (b) is oriented along the radius vector r; (c) coincides in direction with the magnetic field produced by the current I at the point where the loop is located. |
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| 915 | A small current-carrying coil having a magnetic moment pm is located at the axis of a round loop of radius R with current I flowing through it. Find the magnitude of the vector force applied to the coil if its distance from the centre of the loop is equal to x and the vector pm coincides in direction with the axis of the loop. |
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| 916 | Find the interaction force of two coils with magnetic moments p1m = 4.0 mA*m2 and p2m = 6.0 mA*m2 and collinear axes if the separation between the coils is equal to l = 20 cm which exceeds considerably their linear dimensions. |
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| 917 | A permanent magnet has the shape of a sufficiently thin disc magnetized along its axis. The radius of the disc is R = 1.0 cm. Evaluate the magnitude of a molecular current I' flowing along the rim of the disc if the magnetic induction at the point on the axis of the disc, lying at a distance x = 10 cm from its centre, is equal to B = 30 RT. |
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| 918 | The magnetic induction in vacuum at a plane surface of a uniform isotropic magnetic is equal to B, the vector B forming an angle α with the normal of the surface. The permeability of the magnetic is equal to μ. Find the magnitude of the magnetic induction B' in the magnetic in the vicinity of its surface. |
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| 919 | The magnetic induction in vacuum at a plane surface of a magnetic is equal to B and the vector B forms an angle θ with the normal n of the surface (Fig. 3.74). The permeability of the magnetic is equal to μ. Find: (a) the flux of the vector H through the spherical surface S of radius R, whose centre lies on the surface of the magnetic; (b) the circulation of the vector B around the square path Γ with side l located as shown in the figure. |
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| 920 | A direct current I flows in a long round uniform cylindrical wire made of paramagnetic with susceptibility x. Find: (a) the surface molecular current I's; (b) the volume molecular current I'v. How are these currents directed toward each other? |
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