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2. Two conducting semicircles, MN and MO, centered at points O and O1 respectively, are placed on a horizontal plane. The radii of the two semicircles are 4 cm and 2 cm, respectively. The two semicircles are in electrical contact at point M. A uniform magnetic field normal to the horizontal plane exists in the region enclosed by the two semicircles and the line ON, as shown in Figure 2. The magnitude of the magnetic field is B = 0.015 T. An ultrathin conducting rod has one end electrically connected to the smaller semicircle MO at point O, and is fixed at point O0. The rod has a length equals to the radius of the larger semicircle, and it rotates clockwise around O at a constant angular velocity o = 50 t rad/s. During the rotation, the other end of the rod, labelled as P, is in good electrical contact with the larger semicircle MN. At t = 0, the end of the rod P is at point M. For 0sis“, as the rod rotates, it is also in good electrical contact with the 20 smaller semicircle MO at some point Q, as shown in Figure 2. Assume that the conducting rod has a uniform resistance per unit length, A = 5 Q/m. Neglect the resistance of the two semicircles. X X X X X X X X X X _ N X X M O1 Figure 2 (i) Determine the direction of the current flow in the loop MPQM while the rod is rotating. (ii) Express the emf induced in the loop MPQM as a function of t and the magnitude of the magnetic force acting on the conducting rod OP for 0

2. Two conducting semicircles, MN and MO, centered at points O and O1 respectively, are placed on a horizontal plane. The radii of the two semicircles are 4 cm and 2 cm, respectively. The two semicircles are in electrical contact at point M. A uniform magnetic field normal to the horizontal plane exists in the region enclosed by the two semicircles and the line ON, as shown in Figure 2. The magnitude of the magnetic field is B = 0.015 T. An ultrathin conducting rod has one end electrically connected to the smaller semicircle MO at point O, and is fixed at point O0. The rod has a length equals to the radius of the larger semicircle, and it rotates clockwise around O at a constant angular velocity o = 50 t rad/s. During the rotation, the other end of the rod, labelled as P, is in good electrical contact with the larger semicircle MN. At t = 0, the end of the rod P is at point M. For 0sis“, as the rod rotates, it is also in good electrical contact with the 20 smaller semicircle MO at some point Q, as shown in Figure 2. Assume that the conducting rod has a uniform resistance per unit length, A = 5 Q/m. Neglect the resistance of the two semicircles. X X X X X X X X X X _ N X X M O1 Figure 2 (i) Determine the direction of the current flow in the loop MPQM while the rod is rotating. (ii) Express the emf induced in the loop MPQM as a function of t and the magnitude of the magnetic force acting on the conducting rod OP for 0

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2. Two conducting semicircles, MN and MO, centered at points O and O1 respectively, are placed on a horizontal plane. The radii of the two semicircles are 4 cm and 2 cm, respectively. The two semicircles are in electrical contact at point M. A uniform magnetic field normal to the horizontal plane exists in the region enclosed by the two semicircles and the line ON, as shown in Figure 2. The magnitude of the magnetic field is B = 0.015 T. An ultrathin conducting rod has one end electrically connected to the smaller semicircle MO at point O, and is fixed at point O0. The rod has a length equals to the radius of the larger semicircle, and it rotates clockwise around O at a constant angular velocity o = 50 t rad/s. During the rotation, the other end of the rod, labelled as P, is in good electrical contact with the larger semicircle MN. At t = 0, the end of the rod P is at point M. For 0sis“, as the rod rotates, it is also in good electrical contact with the 20 smaller semicircle MO at some point Q, as shown in Figure 2. Assume that the conducting rod has a uniform resistance per unit length, A = 5 Q/m. Neglect the resistance of the two semicircles. X X X X X X X X X X _ N X X M O1 Figure 2 (i) Determine the direction of the current flow in the loop MPQM while the rod is rotating. (ii) Express the emf induced in the loop MPQM as a function of t and the magnitude of the magnetic force acting on the conducting rod OP for 0<ts. (ii) Find the magnitude of the magnetic force acting on the conducting rod OP for I sis. 20 (iv) Find the work done against the magnetic force from t 0 to t=". 1- cos 2x) Hint: Useful integration, dx%3D2x +sin xr- sin 2x-sin 3x+ C 1- cos x 3
Transcribed Image Text:2. Two conducting semicircles, MN and MO, centered at points O and O1 respectively, are placed on a horizontal plane. The radii of the two semicircles are 4 cm and 2 cm, respectively. The two semicircles are in electrical contact at point M. A uniform magnetic field normal to the horizontal plane exists in the region enclosed by the two semicircles and the line ON, as shown in Figure 2. The magnitude of the magnetic field is B = 0.015 T. An ultrathin conducting rod has one end electrically connected to the smaller semicircle MO at point O, and is fixed at point O0. The rod has a length equals to the radius of the larger semicircle, and it rotates clockwise around O at a constant angular velocity o = 50 t rad/s. During the rotation, the other end of the rod, labelled as P, is in good electrical contact with the larger semicircle MN. At t = 0, the end of the rod P is at point M. For 0sis“, as the rod rotates, it is also in good electrical contact with the 20 smaller semicircle MO at some point Q, as shown in Figure 2. Assume that the conducting rod has a uniform resistance per unit length, A = 5 Q/m. Neglect the resistance of the two semicircles. X X X X X X X X X X _ N X X M O1 Figure 2 (i) Determine the direction of the current flow in the loop MPQM while the rod is rotating. (ii) Express the emf induced in the loop MPQM as a function of t and the magnitude of the magnetic force acting on the conducting rod OP for 0<ts. (ii) Find the magnitude of the magnetic force acting on the conducting rod OP for I sis. 20 (iv) Find the work done against the magnetic force from t 0 to t=". 1- cos 2x) Hint: Useful integration, dx%3D2x +sin xr- sin 2x-sin 3x+ C 1- cos x 3
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