CHAPTER 22ELECTROMAGNETIC INDUCTIONCONCEPTUAL QUESTIONS_____________________________________________________________________________________________1. REASONING AND SOLUTION If the coil and the magnet in Figure 22.1a were each moving withthe same velocity relative to the earth, there would be no relative motion between the magnet and thecoil. The magnetic flux through the coil due to the bar magnet would be constant and, therefore, thecombined motion of the bar magnet and the coil would not result in an induced current in the coil.We are ignoring here any effect due to the earth's magnetic field._____________________________________________________________________________________________2. REASONING AND SOLUTION In the discussion concerning Figure 22.5, we saw that a force of0.086 N from an external agent was required to keep the rod moving at constant speed. Suppose thelight bulb in the figure is unscrewed from its socket. Once the light bulb is unscrewed, theconducting rails and the rod are no longer part of a complete circuit (the resistance of the emptysocket is infinite). Therefore, even though there will be a charge separation and a motional emf in therod given by vBL, there will be no current in the rod. Since there is no current, there is no magneticforce to resist the motion of the rod. From Newton's first law, the rod will continue to move withconstant velocity v without the application of an external force._____________________________________________________________________________________________3. REASONING AND SOLUTION A metal sheet moves to the right at a velocity v in a magneticfield B that is directed into the sheet. At the instant shown in the figure, the magnetic field onlyextends over half of the sheet. An induced emf leads to the eddy current shown.(into page)BvMetal sheetEddy currentxx xxx xxx xxx xx x xWe can apply RHR-1 (modified for currents) to the portion of the eddy current that exists in theportion of the sheet that is in the magnetic field. With the thumb of the right hand pointing towardthe top of the page (direction of I ), and the fingers of the right hand pointing into the page (directionof B), the palm of the right hand faces the left (direction of F). Thus, there is a retarding magneticforce F that acts on the sheet due to the interaction of the eddy current with the magnetic field.Hence, the eddy current causes the sheet to slow down._____________________________________________________________________________________________Chapter 22 Conceptual Questions 1274. REASONING AND SOLUTION A magnetic field B is necessary if there is to be a magneticflux Φ passing through a coil of wire. Yet, just because there is a magnetic field does not mean that amagnetic flux will pass through a coil.The general expression for magnetic flux is given by Equation 22.2: Φ=(B cos φ)A, where B is themagnitude of the magnetic field, A is the cross-sectional area of the coil, and φ is the angle betweenthe magnetic field B and the normal to the surface of the coil. Equation 22.2 shows that the fluxdepends only on the component of the magnetic field that is perpendicular to the surface of the coil.As shown in Example 4 and in Figure 22.11, when the coil is oriented so that it is parallel to the field,φ = 90°, B has no component normal to the surface of the coil, and the magnetic flux through the coilis zero. Therefore, the magnetic flux through a coil can be zero even though there is a magnetic fieldpresent._____________________________________________________________________________________________5. REASONING AND SOLUTION It is known that the magnetic flux through a 1-m2 flat surface is 2Wb. From this data alone, it is possible to determine certain information about the average magneticfield at the surface, but not the magnitude and direction of the field.The general expression for the magnetic flux through the surface is given by Equation 22.2:Φ=(B cos φ)A, where B is the magnitude of the magnetic field, A is the cross-sectional area of thesurface, and φ is the angle between the magnetic field B and the normal to the surface. Equation 22.2shows that the flux depends only on the component of the magnetic field that is perpendicular to thesurface. Therefore, from the information given, we can only ascertain that the component of themagnetic field that is perpendicular to the surface has an average magnitude of 2 T._____________________________________________________________________________________________6. REASONING AND SOLUTION Initially, before the switch is closed, neither the conducting railsnor the rod carries a current. When the switch is closed, a conventional current will flow along theconducting rails from the positive toward the negative terminal of the battery. Since the rod is aconducting rod, current will flow through the rod, from top to bottom. According to RHR-1, therewill be a force that points to the right on the conducting rod due to the magnetic field; therefore, therod will be pushed and accelerate to the right. As the rod moves to the right, the area bound by the"loop" increases, thereby increasing the magnetic flux through the loop. As the magnetic fluxincreases, an induced emf appears around the "loop." According to Lenz's law, the induced emf thatappears, will appear in such a way so as to oppose the increase in the magnetic flux. This will occurif the induced emf opposes the battery emf, with the result that the current in the rod begins todecrease and reaches zero when the induced emf exactly offsets the battery emf. With no current inthe rod, there is no longer a magnetic force applied to the rod. With no force, there is zeroacceleration. In other words, from this point on, the rod moves with a constant velocity._____________________________________________________________________________________________7. REASONING AND SOLUTION A bolt of lightning contains moving charges, and hence, is acurrent. This current is surrounded by its magnetic field. Since the charges in a bolt of lightningmove erratically, the current is a time-dependent and gives rise to a time-dependent magnetic field.Many household appliances contain coils. If the time-dependent magnetic field passes through thesecoils, the magnetic flux through the coils will be time-dependent. From Faraday's law, there will bean induced emf and, hence, an induced current in the coils of the appliance. This will result in