29a. Electromagnetic InductionConceptual InductionPart AWhat is the direction of the induced current in the loop when the loop is above the solenoid, moving downward?clockwiseCorrect Part BWhat is the direction of the induced current when the loop is at the midpoint of the solenoid and still moving downward?no currentCorrect Part CWhat is the direction of the induced current when the loop is below the solenoid and moving downward?counterclockwiseCorrect Introduction to Farada!s "awPart AConsider the direction of the electric field in the figure# Assume that the magnetic field points upward, as shown# $nder what circumstances is the direction of the electric field shown in the figure correct?ifdecreases with timeCorrect Part B%ow consider the magnetic flu& through a surface bounded b the loop# Which of the following statements about this surface must be true if ou want to use Farada!s law to relate the magnetic flu& to the line integral of the electric field around the loop?'he surface can be an surface whose edge is the loop#Correct (ou are free to take an surface bounded b the loop as the surface over which to evaluate the integral# 'he result will alwas be the same, owing to the continuit of magnetic field lines )the never start or end anwhere, since there are no magnetic charges*# It is important to understand the vast differences between electric fields produced b changing magnetic fields via Farada!s law and the more familiar electric fields producedb charges via Coulomb!s law# +ere are some short ,uestions that illustrate these differences#Part CWhen can an electric field be measured at an point from the force on a stationar test charge at that point?no matter how the field is generatedCorrect In fact, this operation defines an electric field# -imilarl, if the test charge is moving, it will measure magnetic fields# Part .When can an electric field that does not var in time arise?in either of the above two casesCorrect Part /When will the integralaround an closed loop of the pro0ection of the electric field along that loop be 1ero?onl if the field is generated b the coulomb field of charges that are static or moving in astraight lineCorrect 'he electric field generated b a uniforml moving charge is 0ust the moving field of a static charge, which alwas has 1ero loop integral# +ere is a simple ,uantitative problem that uses Farada!s law#Part FA clindrical iron rod of infinite length with cross2sectional areais oriented with its a&is of smmetr coincident with the z a&is of a clindrical coordinate sstem as shown in the figure# It has a magnetic field inside that varies according to# Findthe theta componentof the electric field at distancefrom the z a&is, whereis larger than the radius of the rod# /&press our answer in terms of,,,, and an needed constants such as,, and#3)2A4B56*7)84pi49*Correct 29b. Electromagnetic Induction9ail :unPart AA conducting rod is free to slide on two parallel rails with negligible friction# At the right end of the rails, a voltage source of strengthin series with a resistor of resistance makes a closed circuit together with the rails and the rod# 'he rails and the rod are taken to be perfect conductors# 'he rails e&tend to infinit on the left# 'he arrangement is shown in the figure#

'here is a uniform magnetic field of magnitude, pervading all space, perpendicular to the plane of rod and rails# 'he rod is released from rest, and it is observed that it accelerates to the left# In what direction does the magnetic field point?out of the plane of the figureCorrect Part BAssuming that the rails have no resistance, what is the most accurate ,ualitative description of the motion of the rod?'he rod will accelerate but the magnitude of the acceleration will decrease with time; the velocit of the rod will approach but never e&ceed a certain terminal velocit#Correct Part CWhat is the accelerationof the rod? 'aketo be the mass of the rod#/&press our answer as a function of,, the velocit of the rod,,, and the mass of the rod#3)))#'o achieve a high acceleration, which is necessar for a useful gun, a magnetic field of large magnitude and a high voltage are advantageous# Part .What is the terminal velocitreached b the rod?3