| № |
Condition |
free/or 0.5$ |
| 921 | Half of an infinitely long straight current-carrying solenoid is filled with magnetic substance as shown in Fig. 3.75. Draw the approximate plots of magnetic induction B, strength H, and magnetization J on the axis as functions of x. |
|
| 922 | An infinitely long wire with a current I flowing in it is located in the boundary plane between two non-conducting media with permeabilities μ1 and μ2. Find the modulus of the magnetic induction vector throughout the space as a function of the distance r from the wire. It should be borne in mind that the lines of the vector B are circles whose centres lie on the axis of the wire. |
|
| 923 | A round current-carrying loop lies in the plane boundary between magnetic and vacuum. The permeability of the magnetic is equal to R. Find the magnetic induction B at an arbitrary point on the axis of the loop if in the absence of the magnetic the magnetic induction at the same point becomes equal to B0. Generalize the obtained result to all points of the field. |
|
| 924 | When a ball made of uniform magnetic is introduced into an external uniform magnetic field with induction B0, it gets uniformly magnetized. Find the magnetic induction B inside the ball with permeability μ; recall that the magnetic field inside a uniformly magnetized ball is uniform and its strength is equal to H' = -J/3, where J is the magnetization. |
|
| 925 | N = 300 turns of thin wire are uniformly wound on a permanent magnet shaped as a cylinder whose length is equal to L = = 15 cm. When a current I = 3.0 A was passed through the wiring the field outside the magnet disappeared. Find the coercive force He of the material from which the magnet was manufactured. |
|
| 926 | A permanent magnet is shaped as a ring with a narrow gap between the poles. The mean diameter of the ring equals d = 20 cm. The width of the gap is equal to b = 2.0 mm and the magnetic induction in the gap is equal to B = 40 mT. Assuming that the scattering of the magnetic flux at the gap edges is negligible, find the modulus of the magnetic field strength vector inside the magnet. |
|
| 927 | An iron core shaped as a tore with mean radius R = 250 mm supports a winding with the total number of turns N = 1000. The core has a cross-cut of width b = 1.00 mm. With a current I = 0.85 A flowing through the winding, the magnetic induction in the gap is equal to B = 0.75 T. Assuming the scattering of the magnetic flux at the gap edges to be negligible, find the permeability of iron under these conditions. |
|
| 928 | Fig. 3.76 illustrates a basic magnetization curve of iron (commercial purity grade). Using this plot, draw the permeability m as a function of the magnetic field strength H. At what value of H is the permeability the greatest? What is m max, equal to? |
|
| 929 | A thin iron ring with mean diameter d = 50 cm supports a winding consisting of N = 800 turns carrying current I = 3.0 A. The ring has a cross-cut of width b = 2.0 mm. Neglecting the scattering of the magnetic flux at the gap edges, and using the plot shown in Fig. 3.76, find the permeability of iron under these conditions. |
|
| 930 | A long thin cylindrical rod made of paramagnetic with magnetic susceptibility χ and having a cross-sectional area S is located along the axis of a current-carrying coil. One end of the rod is located at the coil centre where the magnetic induction is equal to B whereas the other end is located in the region where the magnetic field is practically absent. What is the force that the coil exerts on the rod? |
|
| 931 | In the arrangement shown in Fig. 3.77 it is possible to measure (by means of a balance) the force with which a paramagnetic ball of volume V = 41 mm3 is attrabted to a pole of the electromagnet M. The magnetic induction at the axis of the poleshoe depends on the height x as B = B0 exp(-ax2), where B0 = 1.50 T, a = 100 m-2. Find: (a) at what height xm the ball experiences the maximum attraction; (b) the magnetic susceptibility of the paramagnetic if the maximum attraction force equals Fmax = 160 μN. |
|
| 932 | A small ball of volume V made of paramagnetic with susceptibility x was slowly displaced along the axis of a current-carrying coil from the point where the magnetic induction equals B out to the region where the magnetic field is practically absent. What amount of work was performed during this process? |
|
| 933 | A wire bent as a parabola y = ax2 is located in a uniform magnetic field of induction B, the vector B being perpendicular to the plane x, y. At the moment t = 0 a connector starts sliding translationwise from the parabola apex with a constant acceleration w (Fig. 3.78). Find the emf of electromagnetic induction in the loop thus formed as a function of y. |
|
| 934 | A rectangular loop with a sliding connector of length l is located in a uniform magnetic field perpendicular to the loop plane (Fig. 3.79). The magnetic induction is equal to B. The connector has an electric resistance R, the sides AB and CD have resistances R1 and R2 respectively. Neglecting the self-inductance of the loop, find the current flowing in the connector during its motion with a constant velocity v. |
|
| 935 | A metal disc of radius a = 25 cm rotates with a constant angular velocity ω = 130 rad/s about its axis. Find the potential difference between the centre and the rim of the disc if (a) the external magnetic field is absent; (b) the external uniform magnetic field of induction B = 5.0 mT is directed perpendicular to the disc. |
|
| 936 | A thin wire AC shaped as a semi-circle of diameter d = 20 cm rotates with a constant angular velocity w = 100 rad/s in a uniform magnetic field of induction B = 5.0 mT, with w || B. The rotation axis passes through the end A of the wire and is perpendicular to the diameter AC. Find the value of a line integral E dr along the wire from point A to point C. Generalize the obtained result. |
|
| 937 | A wire loop enclosing a semi-circle of radius a is located on the boundary of a uniform magnetic field of induction B (Fig. 3.80). At the moment t = 0 the loop is set into rotation with a constant angular acceleration p about an axis O coinciding with a line of vector B on the boundary. Find the emf induced in the loop as a function of time t. Draw the approximate plot of this function. The arrow in the figure shows the emf direction taken to be positive. |
|
| 938 | A long straight wire carrying a current I and a Π-shaped conductor with sliding connector are located in the same plane as shown in Fig. 3.81. The connector of length l and resistance R slides to the right with a constant velocity v. Find the current induced in the loop as a function of separation r between the connector and the straight wire. The resistance of the Π-shaped conductor and the self-inductance of the loop are assumed to be negligible. |
|
| 939 | A square frame with side a and a long straight wire carrying a current I are located in the same plane as shown in Fig. 3.82. The frame translates to the right with a constant velocity v. Find the emf induced in the frame as a function of distance x. |
|
| 940 | A metal rod of mass m can rotate about a horizontal axis 0, sliding along a circular conductor of radius a (Fig. 3.83). The arrangement is located in a uniform magnetic field of induction B directed perpendicular to the ring plane. The axis and the ring are connected to an emf source to form a circuit of resistance R. Neglecting the friction, circuit inductance, and ring resistance, find the law according to which the source emf must vary to make the rod rotate with a constant angular velocity w. |
|
