| № |
Condition |
free/or 0.5$ |
| 881 | A single-layer coil (solenoid) has length l and cross-section radius R. A number of turns per unit length is equal to n. Find the magnetic induction at the centre of the coil when a current I flows through it. |
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| 882 | A very long straight solenoid has a cross-section radius R and n turns per unit length. A direct current I flows through the solenoid. Suppose that x is the distance from the end of the solenoid, measured along its axis. Find: (a) the magnetic induction B on the axis as a function of x; draw an approximate plot of B vs the ratio x/R; (b) the distance x0 to the point on the axis at which the value of B differs by η = 1% from that in the middle section of the solenoid. |
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| 883 | A thin conducting strip of width h = 2.0 cm is tightly wound in the shape of a very long coil with cross-section radius R = 2.5 cm to make a single-layer straight solenoid. A direct current I = 5.0 A flows through the strip. Find the magnetic induction inside and outside the solenoid as a function of the distance r from its axis. |
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| 884 | N = 2.5·10^3 wire turns are uniformly wound on a wooden toroidal core of very small cross-section. A current I flows through the wire. Find the ratio 1 of the magnetic induction inside the core to that at the centre of the toroid. |
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| 885 | A direct current I = 10 A flows in a long straight round conductor. Find the magnetic flux through a half of wire's cross-section per one metre of its length. |
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| 886 | A very long straight solenoid carries a current I. The cross-sectional area of the solenoid is equal to S, the number of turns per unit length is equal to n. Find the flux of the vector B through the end plane of the solenoid. |
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| 887 | Fig. 3.65 shows a toroidal solenoid whose cross-section is rectangular. Find the magnetic flux through this cross-section if the current through the winding equals I = 1.7 A, the total number of turns is N = 1000, the ratio of the outside diameter to the inside one is η = 1.6, and the height is equal to h = 5.0 cm. |
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| 888 | Find the magnetic moment of a thin round loop with current if the radius of the loop is equal to R = 100 mm and the magnetic induction at its centre is equal to B = 6.0 μT. |
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| 889 | Calculate the magnetic moment of a thin wire with a current I = 0.8 A, wound tightly on half a tore (Fig. 3.66). The diameter of the cross-section of the tore is equal to d = 5.0 cm, the number of turns is N = 500. |
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| 890 | A thin insulated wire forms a plane spiral of N = 100 tight turns carrying a current I = 8 mA. The radii of inside and outside turns (Fig. 3.67) are equal to a = 50 mm and b = 100 mm. Find: (a) the magnetic induction at the centre of the spiral; (b) the magnetic moment of the spiral with a given current. |
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| 891 | A non-conducting thin disc of radius R charged uniformly over one side with surface density σ rotates about its axis with an angular velocity ω. Find: (a) the magnetic induction at the centre of the disc; (b) the magnetic moment of the disc. |
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| 892 | A non-conducting sphere of radius R = 50 mm charged uniformly with surface density σ = 10.0 μC/m2 rotates with an angular velocity ω = 70 rad/s about the axis passing through its centre. Find the magnetic induction at the centre of the sphere. |
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| 893 | A charge q is uniformly distributed over the volume of a uniform ball of mass m and radius R which rotates with an angular velocity ω about the axis passing through its centre. Find the respective magnetic moment and its ratio to the mechanical moment. |
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| 894 | A long dielectric cylinder of radius R is statically polarized so that at all its points the polarization is equal to P = ar, where a is a positive constant, and r is the distance from the axis. The cylinder is set into rotation about its axis with an angular velocity w. Find the magnetic induction B at the centre of the cylinder. |
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| 895 | Two protons move parallel to each other with an equal velocity v = 300 km/s. Find the ratio of forces of magnetic and electrical interaction of the protons. |
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| 896 | Find the magnitude and direction of a force vector acting on a unit length of a thin wire, carrying a current I = 8.0 A, at a point O, if the wire is bent as shown in (a) Fig. 3.68a, with curvature radius R = 10 cm; (b) Fig. 3.68b, the distance between the long parallel segments of the wire being equal to l = 20 cm. |
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| 897 | A coil carrying a current I = 10 mA is placed in a uniform magnetic field so that its axis coincides with the field direction. The single-layer winding of the coil is made of copper wire with diameter d = 0.10 mm, radius of turns is equal to R = 30 mm. At what value of the induction of the external magnetic field can the coil winding be ruptured? |
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| 898 | A copper wire with cross-sectional area S = 2.5 mm2 bent to make three sides of a square can turn about a horizontal axis OO' (Fig. 3.69). The wire is located in uniform vertical magnetic field. Find the magnetic induction if on passing a current I = 16 A through the wire the latter deflects by an angle θ = 20°. |
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| 899 | A small coil C with N = 200 turns is mounted on one end of a balance beam and introduced between the poles of an electromagnet as shown in Fig. 3.70. The cross-sectional area of the coil is S =1.0 cm2, the length of the arm OA of the balance beam is l = 30 cm. When there is no current in the coil the balance is in equilibrium. On passing a current I = 22 mA through the coil the equilibrium is restored by putting the additional counterweight of mass Δm = 60 mg on the balance pan. Find the magnetic induction at the spot where the coil is located. |
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| 900 | A square frame carrying a current I = 0.90 A is located in the same plane as a long straight wire carrying a current I0 = 5.0 A. The frame side has a length a = 8.0 cm. The axis of the frame passing through the midpoints of opposite sides is parallel to the wire and is separated from it by the distance which is η = 1.5 times greater than the side of the frame. Find: (a) Ampere force acting on the frame; (b) the mechanical work to be performed in order to turn the frame through 180° about its axis, with the currents maintained constant. |
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