Physics 2 - Lecture 4: Electromagnetism 2 - Pham Tan Thi

Nội dung text: Physics 2 - Lecture 4: Electromagnetism 2 - Pham Tan Thi

1. Magnetic Fields
2. Magnetic Field Lines q Magnetic filed lines outside the magnet point away from the north pole and toward the south pole.
3. Magnetic Force q The magnetic field is defined in terms of the force acting on a moving charged particle q The magnitude of the magnetic force on a charged particle is
4. An Electron Moving in a Magnetic Field q An electron in an old-style television picture tube moves toward the front of the tube with a speed of 8.0 x 106 m/s along the x axis (Fig. 29.6). Surrounding the neck of the tube are coils of wire that create a magnetic field of magnitude 0.025 T, directed at an angle of 60° to the x axis and lying in the xy plane. Calculate the magnetic force on the electron.
5. Representations of Magnetic Field Lines Perpendicular to the Page
6. Motion of a Charged Particle in a Uniform Magnetic Field q Newton 2nd Law: q The particle moves in a circle, we also model it as a particle in uniform circular motion q The radius of the circular path: q The angular speed of the particle: Counterclockwise for a positive charge Clockwise for negative charge
7. Motion of a Charged Particle in a Non- Uniform Magnetic Field
8. Magnetic Force Acting on a Current- Carrying Conductor q The magnetic force exerted on a charge q moving with a drift velocity is q The total magnetic force on the segment of wire of length L is • L: wire length • A: cross-sectional area • n: number of mobile charge carriers
9. Force on a Semicircular Conductor qA wire bent into a semicircle of radius R forms a closed circuit and carries a current I. The wire lies in the xy plane, and a uniform magnetic field is directed along the positive y axis as in Figure. Find the magnitude and direction of the magnetic force acting on the straight portion of the wire and on the curved portion.
10. Torque on a Current Loop in a Uniform Magnetic Field q Consider a rectangular loop carrying a current I in the presence of a uniform magnetic field directed parallel to the plane of the loop as shown in Figure. q No magnetic forces act on sides (1) and (3) because these wires are parallel to the field q Magnetic forces act on sides (2) and (4) because these sides are oriented perpendicular to the field.
11. Torque on a Current Loop in a Uniform Magnetic Field q Supposing the uniform magnetic field makes angle θ < 90° q Assuming B is perpendicular to sides (2) and (4) q Magnetic forces F1 and F3 exerted on sides (1) and (3) cancel out. q Magnetic forces F2 and F4 exerted on sides (2) and (4) produce a torque about any point. F2 = (b/2)sinθ F4 = (b/2)sinθ F2 = F4 = IaB
12. Potential Energy of a Magnetic Dipole in Magnetic Field q Recall the potential energy of an electric dipole in electric field is (this energy depends on the orientation of the dipole in the electric field) q Similarly, the potential energy of a system of a magnetic dipole in a magnetic field depends on the orientation of the dipole in the magnetic field
13. The Magnetic Dipole Moment in a Coil q A rectangular coil of dimensions 5.40 x 8.50 cm consists of 25 turns of wire and carries a current of 15.0 mA. A 0.350-T magnetic field is applied parallel to the plane of the coil. (A)Calculate the magnitude of the magnetic dipole moment of the coil (B)What is the magnitude of the torque acting on the loop?
14. Currents Create Magnetic Fields q 1820: Oersted did an experiment à a magnetic compass is deflected by current à magnetic field are due to currents Why do the un-magnetized filings line up with the field? In fact, currents are the only way to create magnetic fields.
15. The Biot-Savart Law q The total magnetic field B is a sum up contributions from all current elements Ids that make up the current is an integral Special care for the integrand of cross product q The integral is taken over the entire current distribution. q The magnitude of the magnetic field is inversely proportional to the square of the distance r (similar to electric field). q Direction of electric field is radial q Direction of magnetic field is perpendicular to length ds and unit vector r-hat
16. Magnetic Field Surrounding a Thin, Straight Conductor q Consider a thin, straight wire of finite length carrying a constant current I and placed along the x axis as shown in Figure 30.3. Determine the magnitude and direction of the magnetic field at point P due to this current.
17. Magnetic Field Surrounding a Thin, Straight Conductor q If the wire becomes infinitely long, we see that θ1 = π/2 and θ2 = -π/2 and hence (sinθ1 – sinθ2) = [sin π/2 – sin(-π/2)] = 2
18. Magnetic Field due to a Curved Wire Segment q Calculate the magnetic field at point O for the current- carrying wire segment shown in Figure 30.4. The wire consists of two straight portions and a circular arc of radius a, which subtends an angle θ.
19. Magnetic Field on the Axis of a Circular Current Loop q Consider a circular wire loop of radius a located in the yz plane and carrying a steady current I as in Figure 30.5. Calculate the magnetic field at an axial point P a distance x from the center of the loop.
20. The magnetic Force Between to Parallel Conductors q The magnetic force on a length l of wire 1 q l is perpendicular to B2, the magnitude of F1 is q The direction of F1 is toward to wire 2 because l x B is in that direction. The magnitude of force per unit length
21. Magnetic Field Created by a Long Current- Carrying Wire A long, straight wire of radius R carries a steady current I that is uniformly distributed through the cross section of the wire (Fig. 30.13). Calculate the magnetic field a distance r from the center of the wire in the regions r R.
22. Magnetic Field Created by a Long Current- Carrying Wire A long, straight wire of radius R carries a steady current I that is uniformly distributed through the cross section of the wire (Fig. 30.13). Calculate the magnetic field a distance r from the center of the wire in the regions r R. (The current I’ passing through the plane of circle 2 is less than the total current I)
23. Magnetic Field Created by a Toroid q A device called a toroid (Fig. 30.15) is often used to create an almost uniform magnetic field in some enclosed area. The device consists of a conducting wire wrapped around a ring (a torus) made of a non-conducting material. For a toroid having N closely spaced turns of wire, calculate the magnetic field in the region occupied by the torus, a distance r from the center.
24. Magnetic Field of a Solenoid q A solenoid is a long wire wound in the form of a helix à to create a reasonably uniform magnetic field in the space surrounded by turns of wire
25. Magnetic Flux q The total magnetic flux !B through the surface of area A is q The total magnetic flux !B is then q θ = 90° (B is perpendicular to A), !B is zero q θ = 0° (B is parallel to A), !B is maximum
26. Magnetic Flux through a Rectangular Loop q A rectangular loop of width a and length b is located near a long wire carrying a current I (Fig. 30.21). The distance between the wire and the closest side of the loop is c. The wire is parallel to the long side of the loop. Find the total magnetic flux through the loop due to the current in the wire.
27. Gauss’s Law in Magnetism q The net magnetic flux through any closed surface is always zero:
28. Faraday’s Law of Induction q The emf is directly proportional to the time rate of the change of the magnetic flux through the loop. q Faraday’s law of induction: q If a coil consists of N loops: q For a loop enclosing an area A lies in uniform magnetic field B
29. Inducing an emf in a Coil q A coil consists of 200 turns of wire. Each turn is a square of side d = 18 cm, and a uniform magnetic field directed perpendicular to the plane of the coil is turned on. If the field changes linearly from 0 to 0.50 T in 0.80 s, what is the magnitude of the induced emf in the coil while the field is changing?