MIT OpenCourseWare http://ocw.mit.edu Electromagnetic Field Theory: A Problem Solving Approach For any use or distribution of this textbook, please cite as follows: Markus Zahn, Electromagnetic Field Theory: A Problem Solving Approach. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). License: Creative Commons Attribution-NonCommercial-Share Alike. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.chapter 2the electricfield50 The Electric FieldThe ancient Greeks observed that when the fossil resinamber was rubbed, small light-weight objects were attracted.Yet, upon contact with the amber, they were then repelled.No further significant advances in the understanding of thismysterious phenomenon were made until the eighteenthcentury when more quantitative electrification experimentsshowed that these effects were due to electric charges, thesource of all effects we will study in this text.2-1 ELECTRIC CHARGE2-1-1 Charging by ContactWe now know that all matter is held together by the attrac-tive force between equal numbers of negatively charged elec-trons and positively charged protons. The early researchersin the 1700s discovered the existence of these two species ofcharges by performing experiments like those in Figures 2-1to 2-4. When a glass rod is rubbed by a dry cloth, as in Figure2-1, some of the electrons in the glass are rubbed off onto thecloth. The cloth then becomes negatively charged because itnow has more electrons than protons. The glass rod becomes(b)Figure 2-1 A glass rod rubbed with a dry cloth loses some of its electrons to the cloth.The glass rod then has a net positive charge while the cloth has acquired an equalamount of negative charge. The total charge in the system remains zero.(b)Electric Charge 51positively charged as it has lost electrons leaving behind asurplus number of protons. If the positively charged glass rodis brought near a metal ball that is free to move as in Figure2-2a, the electrons in the ball near the rod are attracted to thesurface leaving uncovered positive charge on the other side ofthe ball. This is called electrostatic induction. There is then anattractive force of the ball to the rod. Upon contact with therod, the negative charges are neutralized by some of thepositive charges on the rod, the whole combination stillretaining a net positive charge as in Figure 2-2b. This transferof charge is called conduction. It is then found that the nowpositively charged ball is repelled from the similarly chargedrod. The metal ball is said to be conducting as charges areeasily induced and conducted. It is important that thesupporting string not be conducting, that is, insulating,otherwise charge would also distribute itself over the wholestructure and not just on the ball.If two such positively charged balls are brought near eachother, they will also repel as in Figure 2-3a. Similarly, theseballs could be negatively charged if brought into contact withthe negatively charged cloth. Then it is also found that twonegatively charged balls repel each other. On the other hand,if one ball is charged positively while the other is chargednegatively, they will attract. These circumstances are sum-marized by the simple rules:Opposite Charges Attract. Like Charges Repel.G(a) (b) (c)Figure 2-2 (al A charged rod near a neutral ball will induce an opposite charge onthe near surface. Since the ball is initially neutral, an equal amount of positive chargeremains on the far surface. Because the negative charge is closer to the rod, it feels astronger attractive force than the repelling force due to the like charges. (b) Uponcontact with the rod the negative charge is neutralized leaving the ball positivelycharged. (c) The like charges then repel causing the ball to deflect away.52 The Electric Field-4-Figure 2-3 (a) Like charged bodies repel while (b) oppositely charged bodies attract.In Figure 2-2a, the positively charged rod attracts thenegative induced charge but repels the uncovered positivecharge on the far end of the ball. The net force is attractivebecause the positive charge on the ball is farther away fromthe glass rod so that the repulsive force is less than theattractive force.We often experience nuisance frictional electrificationwhen we walk across a carpet or pull clothes out of a dryer.When we comb our hair with a plastic comb, our hair oftenbecomes charged. When the comb is removed our hair stillstands up, as like charged hairs repel one another. Oftenthese effects result in sparks because the presence of largeamounts of charge actually pulls electrons from air molecules.2-1-2 Electrostatic InductionEven without direct contact net charge can also be placedon a body by electrostatic induction. In Figure 2-4a we seetwo initially neutral suspended balls in contact acquiringopposite charges on each end because of the presence of acharged rod. If the balls are now separated, each half retainsits net charge even if the inducing rod is removed. The netcharge on the two balls is zero, but we have been able toisolate net positive and negative charges on each ball.(b)INIIIIIIIIIIIIIIIIII11111111111111111111·- -I -Electric Charge 53+z+4(hiFigure 2-4 A net charge can be placed on a body without contact by electrostaticinduction. (a) When a charged body is brought near a neutral body, the near sideacquires the opposite charge. Being neutral, the far side takes on an equal but oppositecharge. (b) If the initially neutral body is separated, each half retains its charge.2-1-3 Faraday's "Ice-Pail" ExperimentThese experiments showed that when a charged conductorcontacted another conductor, whether charged or not, thetotal charge on both bodies was shared. The presence ofcharge was first qualitatively measured by an electroscopethat consisted of two attached metal foil leaves. Whencharged, the mutual repulsion caused the leaves to diverge.In 1843 Michael Faraday used an electroscope to performthe simple but illuminating "ice-pail" experiment illustratedin Figure 2-5. When a charged body is inside a closed isolatedconductor, an equal amount of charge appears on the outsideof the conductor as evidenced by the divergence of the elec-troscope leaves. This is true whether or not the charged bodyhas contacted the inside walls of the surrounding conductor.If it has not, opposite charges are induced on the inside wallleaving unbalanced charge on the
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