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 2 the electricfield 50 The Electric Field The ancient Greeks observed that when the fossil resin amber 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 this mysterious phenomenon were made until the eighteenth century when more quantitative electrification experiments showed that these effects were due to electric charges the source of all effects we will study in this text 2 1 2 1 1 ELECTRIC CHARGE Charging by Contact We now know that all matter is held together by the attractive force between equal numbers of negatively charged electrons and positively charged protons The early researchers in the 1700s discovered the existence of these two species of charges by performing experiments like those in Figures 2 1 to 2 4 When a glass rod is rubbed by a dry cloth as in Figure 2 1 some of the electrons in the glass are rubbed off onto the cloth The cloth then becomes negatively charged because it now has more electrons than protons The glass rod becomes b 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 equal amount of negative charge The total charge in the system remains zero Electric Charge 51 positively charged as it has lost electrons leaving behind a surplus number of protons If the positively charged glass rod is brought near a metal ball that is free to move as in Figure 2 2a the electrons in the ball near the rod are attracted to the surface leaving uncovered positive charge on the other side of the ball This is called electrostatic induction There is then an attractive force of the ball to the rod Upon contact with the rod the negative charges are neutralized by some of the positive charges on the rod the whole combination still retaining a net positive charge as in Figure 2 2b This transfer of charge is called conduction It is then found that the now positively charged ball is repelled from the similarly charged rod The metal ball is said to be conducting as charges are easily induced and conducted It is important that the supporting string not be conducting that is insulating otherwise charge would also distribute itself over the whole structure and not just on the ball If two such positively charged balls are brought near each other they will also repel as in Figure 2 3a Similarly these balls could be negatively charged if brought into contact with the negatively charged cloth Then it is also found that two negatively charged balls repel each other On the other hand if one ball is charged positively while the other is charged negatively they will attract These circumstances are summarized 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 on the near surface Since the ball is initially neutral an equal amount of positive charge remains on the far surface Because the negative charge is closer to the rod it feels a stronger attractive force than the repelling force due to the like charges b Upon contact with the rod the negative charge is neutralized leaving the ball positively charged c The like charges then repel causing the ball to deflect away 52 The Electric Field INIIIIIIIIIIIIIIIIII11111111111111111111 4 b I Figure 2 3 a Like charged bodies repel while b oppositely charged bodies attract In Figure 2 2a the positively charged rod attracts the negative induced charge but repels the uncovered positive charge on the far end of the ball The net force is attractive because the positive charge on the ball is farther away from the glass rod so that the repulsive force is less than the attractive force We often experience nuisance frictional electrification when we walk across a carpet or pull clothes out of a dryer When we comb our hair with a plastic comb our hair often becomes charged When the comb is removed our hair still stands up as like charged hairs repel one another Often these effects result in sparks because the presence of large amounts of charge actually pulls electrons from air molecules 2 1 2 Electrostatic Induction Even without direct contact net charge can also be placed on a body by electrostatic induction In Figure 2 4a we see two initially neutral suspended balls in contact acquiring opposite charges on each end because of the presence of a charged rod If the balls are now separated each half retains its net charge even if the inducing rod is removed The net charge on the two balls is zero but we have been able to isolate net positive and negative charges on each ball Electric Charge 53 z 4 hi In Figure 2 4 A net charge can be placed on a body without contact by electrostatic induction a When a charged body is brought near a neutral body the near side acquires the opposite charge Being neutral the far side takes on an equal but opposite charge b If the initially neutral body is separated each half retains its charge 2 1 3 Faraday s Ice Pail Experiment These experiments showed that when a charged conductor contacted another conductor whether charged or not the total charge on both bodies was shared The presence of charge was first qualitatively measured by an electroscope that consisted of two attached metal foil leaves When charged the mutual repulsion caused the leaves to diverge In 1843 Michael Faraday used an electroscope to perform the simple but illuminating ice pail experiment illustrated in Figure 2 5 When a charged body is inside a closed isolated conductor an equal amount of charge appears on the outside of the conductor as evidenced by the divergence of the electroscope leaves This is true whether or not the charged body has contacted the inside walls of the surrounding conductor If it has not opposite charges are induced on the inside wall leaving unbalanced charge on the outside If the charged body is removed the charge on the
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