Physics Week 6(Sem. 2) Name Chapter Summary Magnetism Cont d Motional EMF The current in a coil is called induced current, because it is brought about by a changing magnetic field. And since a source of emf is always needed to produce a current, the coil itself behaves as if it were a source of emf. This emf is called induced emf. Consider a rod of length (L) moving with a constant velocity of (v) perpendicular to a magnetic field (B). Due to RHR 1, the electrons move creating a positive top side and a negative bottom. This separation of charges at the ends of the moving conductor gives rise to an induced emf called a motional emf. The fact that the electrical and magnetic forces balance at equilibrium can be used to determine the magnitude of the motional emf (ε). Therefore after some equation solving the motional emf (ε) is Where ε is in units of volts, v is a velocity in m/s, B is the magnetic field in Tesla (T), and L is the length of the rod in meters. As expected ε=0 when the =0, for no motional emf is developed in a stationary situation. Magnetic Field of a Current carrying wire As a charge moves in an electric field it experiences a magnetic force. Therefore charges moving through a current carrying wire create a magnetic field. The right hand rule #2 can be applied to determine the magnetic field around a wire. If your thumb is placed in the direction of the current then your right hand wraps in the direction of the magnetic field (B). To determine the magnitude of the magnetic field on a long straight current carrying wire the equation below can be applied Where μ 0 is the permeability of free space, and its value is 4π x 10 7 T m/a. I is current in Amps and r is radius in meters. This equation demonstrates why the magnetic field strength gets stronger as you approach the current carrying wire, where r is smaller. Magnetic Field of a Current Loop The right hand rule can also be applied to find the direction of the magnetic field of a current carrying loop. Regardless of where on the loop you apply the right hand rule, the field within the loop points in the same direction, upward. The field lines resemble those of a bar magnet. Solenoids produce a strong magnetic field by combining several loops. The magnetic field in a solenoid increases with current and the number of coils per unit length. When an iron rod is placed inside of the loops, it can be called an electromagnet (see fig. 21 8). Magnetic Force on a Current carrying Wire Just like a charge experiences a magnetic force when it moves through a magnetic field, a current carrying wire also experiences a force when it is placed in a magnetic field. If a straight length of wire of length ( ), carrying a current (I) was in a magnetic field (B), the force it would experience would be: Where F mag would be the force the current carrying wire experienced. This equation is only valid when the current and the magnetic field are at right angles to each other. When applying the right hand rule your thumb will be placed in the direction of the current. If the magnetic field is into the page, then the direction of the magnetic force is to the left (see fig). 2 Ms. N. May
Two parallel conducting wires Two parallel conducting wires exert forces on one another, since a current in a conductor creates its own magnetic field. When the current is in the same direction, the two wires attract to one another. This can be confirmed by the right hand rule. If the current in the two wires are going in opposite directions, the two wires will repel each other (see fig). Induced Current Suppose a bar magnet is pushed into a coil of wire. As the magnet moves into the coil, the strength of the magnetic field within the coils increases, and a current is induced in the circuit. This induced current in turn produces its own magnetic field, whose direction could be found using the right hand rule. As the magnet approaches, the magnetic filed lines passing through the coil increase in strength. The induced current in the coil must be in a direction that produces a magnetic field that opposes the increasing strength of the approaching field. The induced magnetic field is therefore in the direction opposite that of the approaching magnetic field (see fig 22 4 &5). In figure 22 4 the coil and the magnet repel one another and in figure 22 5 they attract one another. Magnetic Flux Magnetic flux is analogous to electric flux, which deals with the electric field and the surface through which it passes. Therefore magnetic flux depends on the magnetic field and the surface through which it passes. Using the equation for motional emf (provided before) it can be rearranged to solve for magnetic flux. After some algebra the motional emf equation appears as Ms. N. May Where BA is the area swept out by the rod moving a distance of x and having a length (l). When the magnetic flux is defined as BA it then takes on the symbol φ. Thus the motional emf equation is Ф Ф Ф In other words the induced emf equals the time rate of change of the magnetic flux. Often this equation is written as Ф/, with the minus sign in it. Assigning the minus is important for universal application of the equation for the following reason. The direction of the current induced in the circuit is such that the magnetic force (F) acts on the rod to oppose its motion, thereby tending to slow down the rod. A general equation for magnetic flux such that the component of the magnetic field is perpendicular to the surface must be used. Thus the magnetic flux equation is Ф ө Where Ф is magnetic flux in units of T m 2 or Weber (Wb). Len z Law The rule for finding the direction of the induces current is called Lenz s law and says the magnetic field of the induced current opposes the change in the applied magnetic field. Note that the field of the induced current does not oppose the applied field but rather the change in the applied field. If the applied field changes, the induced field attempts to keep the total field strength constant, according to the principle of energy conservation. Faraday s law of induction Due to the principle of energy conservation, Lenz s law allows you to determine the direction of an induced current in a circuit. Lenz s law does not provide information on the magnitude of the induced current or the induced emf(electromotive force). To calculate the magnitude of the induced emf, you must use Faraday s law of magnetic induction. For a single loop of a circuit, the equation may be Ф Where N is the number of coils, Ф is the change in magnetic flux for 1 loop, and is the time interval during which the magnetic flux changed.
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1. Two long parallel wires, fixed a distance d apart in space, each carry a current I. The force of attraction between them is F. Which other arrangement of currents in long parallel wires would produce the same force F? (1) a current of 3I and a distance of 6d (2) a current of 6I and a distance of 3d (3) a current of 3I and a distance of 3d (4) a current of 9I and a distance of 3d (5) a current of 3I and a distance of 9d 2. Two particles, with equal charge and equal masses and velocities v 1 and v 2 travel in circular paths in a magnetic field with radii R 1 and R 2 respectively. Which of the following must be true? (1) The velocities must be equal but the radii might not be. (2) R 1 v 1 = R 2 v 2 (3) R 1 v 2 = R 2 v 1 (4) The radii must be equal but the velocities might not be. (5) Both the radii and the velocities must be equal. 3. If two current carrying wires exert a force of 50 N on each other, what force will they feel if the distance between them is halved? (1) 12.5 N (4) 25 N (2) 50 N (5) 200 N (3) 100 N 4. Two long, straight, parallel wires 0.24 m apart are carrying the same current I in the same direction. The force per unit length felt by one wire from the other is 2 N/m. Find the value of the current I. (1) 1.55 10 3 A (4) 2.34 10 4 A (2) 4.55 10 3 A (5) 1.55 10 4 A (3) 2.34 10 3 A 5. If two current carrying wires exert a force of 10 N on each other, what force will they feel if the distance between them is doubled? (1) 20 N (4) 5 N (2) 10 N (5) 2.5 N (3) 40 N 6. Two long, straight, parallel wires are placed a distance d apart. A current of I runs through each, in opposite directions. The force per unit length on each wire is (1) attractive, magnitude (µ 0 /2p)I/d (2) attractive, magnitude (µ 0 /2p)I 2 /d 2 (3) repulsive, magnitude (µ 0 /2p)I 2 /d (4) repulsive, magnitude (µ 0 /2p)I/d (5) repulsive, magnitude (µ 0 /2p)I 2 /d 7. Two long, straight, parallel wires are a distance d apart. Wire A carries a current of I, Wire B carries a current 2I. The ratio of the force on Wire A to the force on Wire B is (1) 1:4 (4) 4:1 (2) 1:1 (5) 1:2 (3) 2:1 8. A wire in the plane of the page carries a current I directed toward the bottom of the page. If the wire is located in a uniform magnetic field B directed out of the page, the force on the wire resulting from the magnetic field is (1) directed to the right (2) directed into the page (3) directed to the left (4) directed out of the page (5) zero 9. A wire in the plane of the page carries a current I directed toward the bottom of the page. If the wire is located in a uniform magnetic field B directed toward the top of the page, the force on the wire resulting from the magnetic field is (1) zero (2) directed into the page (3) directed to the left (4) directed to the right (5) directed out of the page 10. The units J/A can be used to express (1) resistance (2) electric field strength (3) magnetic field strength (4) magnetic flux (5) capacitance
11. Base your answer to the following question on the diagram below. 13. The force acting on long current carrying wire in a magnetic field is affected by all of the following EXCEPT (1) the length of strength of the magnetic field. (2) angle between the wire and the direction of the magnetic field. (3) the voltage across the wire. (4) the current in the wire. (5) the direction of current flow. 12. In the picture above, a segment of length l of a current carrying wire is suspended by a string in a uniform magnetic field going out of the page. What is the tension T on the string? (1) mg + IBl (4) mg IBl (2) mg IB/2 (5) (BI l/2) + mg (3) g + lb A long straight wire of length 20 m with a mass per unit length of 0.25 kg/m is lying across the ground perpendicular to a uniform magnetic field of 4.5 T out of the page as shown in the picture above. How much, and in which direction, must current flow to reduce the normal force on the wire to 0 N? (1) 1.1 A from right to left (2) 0.11 A from left to right (3) 1.1 A from left to right (4) 0.11 A from right to left (5) 0.55 A from right to left 14. Two long parallel wires are fixed at a distance d apart and each carry a current of I. The force of attraction between them is F. If the distance between the wires is doubled and the current in each of the wires is doubled, what is the new force of attraction between the wires? (1) 4F (4) F/2 (2) 2F (5) F/4 (3) F 15. Two long parallel wires carry unequal currents in opposite directions. One of the currents is much greater than the other. Compared to the force felt by the wire with the smaller current the force felt by the wire with the greater current is (1) smaller and in the same direction (2) greater and in the same direction (3) equal and in the same direction (4) equal and in the opposite direction (5) smaller and in the opposite direction 16. The magnetic field due to a long straight wire at a distance d from it has a magnitude B. If the current in the wire is doubled, the magnetic field at a distance d would be. (1) 2B (2) B (3) 1 2 B (4) 4B (5) 1 4 B 17. A long straight wire carries a current of 3 A. Find the magnitude of the magnetic field 6 cm from the wire. (1) 2 10 6 T (4) 1 10 4 T (2) 1 10 5 T (5) 2 10 5 T (3) 1 10 6 T
18. Two long straight intersecting wires carry currents I in the directions shown. 20. Which of the following are true about electromagnetic forces and fields? 19. Which direction is the magnetic field pointed at the point P? (1) into the page (2) the magnetic field at point P is zero. (3) towards the top of the page (4) out of the page (5) towards the bottom of the page Two long, straight, parallel wires are separated by a distance d, as shown above. They each carry a steady current I into the page. At what points in the plane of the page and outside the wires, besides the points at infinity is the magnetic field due to the currents zero. (1) Only at point P (2) At all points on the line connecting the two wires (3) At all points on the line AA' (4) At no points (5) At all points on a circle of radius 2d centered at point P I. The magnetic field lines due to a current-carrying wire radiate away from the wire. II. Electric field lines due to a currentcarrying wire circle the wire and their direction is determined by the right hand rule. III. Magnetic force vectors and electric force vectors for a charged particle always point in opposite directions. (1) I and II only (2) III only (3) I and III only (4) none of the above are true (5) I, II, and III 21. If the resistance of a long straight wire is doubled and the voltage remains constant, the magnetic field produced by the wire (1) the magnetic field is not influenced by a change in resistance (2) decreases by a factor of 2 (3) increased by a factor of 2 (4) decreases by a factor of 4 (5) increase by a factor of 4 22. A charged particle is a certain distance away from a current-carrying wire. The particle is moving at a constant velocity, perpendicular to the magnetic field produced by the wire. If the current traveling through the wire and the velocity of the particle are doubled, the force on the particle (1) remains the same (2) increases by a factor of 4 (3) increases by a factor of 2 (4) decreases by a factor of 4 (5) increases by a factor of 8
23. What is the magnetic field due to a circular loop of wire carrying a current I and having a radius R at the center of the loop? (1) ƒ 0 I/4R (2) ƒ 0 I/2R (3) 2pƒ 0 IR (4) ƒ 0 I/2pR (5) ƒ 0 I/4pR 24. A tightly-wound solenoid has a length of 50 cm and contains a total of 200 turns. If it carries a current of 3 A, what is the magnetic field inside the solenoid? (1) 1200ƒ 0 (2) 600ƒ 0 (3) 300ƒ 0 (4) 2400ƒ 0 (5) 100ƒ 0 25. A square loop of wire with sides of 0.20 m is oriented at an angle of 30º to a constant magnetic field of strength 3.0 T. The magnetic flux through this loop is most nearly (1) 6.4 Wb (4) 0.12 Wb (2) 0.06 Wb (5) 75 Wb (3) 0.10 Wb 26. A loop of wire forms a right triangle with legs of length 3 m and 4 m. The loop is placed in a magnetic field of 5 T at a 45 to the magnetic field. What is the magnetic flux through the loop? (1) 26 T m 2 (4) 30 T m 2 (2) 21 T m 2 (5) 15 T m 2 (3) 42 T m 2 27. A straight rod of length 3.0 m is held perpendicular to a magnetic field of 2.0 T. It is rotated about its midpoint at a rate of 5.0 revolutions per second, remaining perpendicular to the field the entire time. The emf generated in the rod is most nearly (1) 141 V (4) 22.5 V (2) 94.2 V (5) 70.7 V (3) 45 V 28. A circular wire loop is at rest in a uniform magnetic field of magnitude 10T that is directed into the page. The loop has a diameter of 6 cm, and the plane of the loop is perpendicular to the field, as shown above. The total magnetic flux through the loop is (1) 6p 10 3 T m 2 (2) 36p 2 10 3 T m 2 (3) 9p 10 3 T m 2 (4) 36p 10 3 T m 2 (5) 0 T m 2 29. Which expression is a unit of potential difference equivalent to a volt? (1) Tesla meter second (2) Tesla meter second 2 (3) Tesla second meter 2 (4) Tesla meter 2 second (5) Tesla second meter 30. The magnetic field from a loop of current carrying wire in the plane of the page is directed out of the page. In which direction do the electrons in the wire loop move? (1) they all move to the left side of the loop (2) counterclockwise (3) clockwise (4) they all move to the right side of the loop (5) they are stationary
31. A conducting loop with a radius of 0.25 m an internal resistance of 4.0Ω is situated in a 12.0 T magnetic field directed into the page as shown. If the area of the loop is shrinking at a rate of 0.05 m 2 /s, what is the induced current in the loop? (1) 0.60 A counterclockwise (2) 0.60 A clockwise (3) 1.2 A clockwise (4) 0.15 A counterclockwise (5) 0.15 A clockwise 32. Base your answer to the following question on the diagram below of two square loops of the same wire, one with side length a and side length 2a. A uniform magnetic field B directed into the page is contained within the area enclosed by the square of side a. 33. A long straight wire has an internal resistance of 2.5 Ω/m. If it moves at 4 m/s in a 5 T magnetic field, what is the magnitude of the force per unit length opposing its motion? (1) 8 N/m (4) 10 N/m (2) 5 N/m (5) 20 N/m (3) 40 N/m 34. Lenz's law concerning induced emf can be shown to directly follow from (1) Conservation of Charge (2) Conservation of Energy (3) Newton's Second Law of Motion (4) Gauss's Law (5) Coulomb's Law 35. A bar magnet is dropped through a loop of wire at a constant velocity. The net amount of current that flowed through a given point in the wire is I when the magnet is exactly halfway through the loop. What is the total amount of current that will have flowed through the same point when the magnet has passed completely through the loop? (1) 2I (4) I (2) I (5) 2I (3) 0 36. Which of the following creates a magnetic field? The magnetic field B varies at a constant rate such that the current induced in the wire with side a is I. Find the current induced in the loop with side 2a. (1) 4I (2) I 2 (3) 2I (4) I 4 (5) I I. Moving electric charges II. Stationary electric charges III. Time changing electric fields (1) III only (4) II and III only (2) I and II only (5) I, II, and III (3) I and III only