We say that concert A corresponds to a frequency of 440 Hz Does that mean that a flute playing concert A is emitting low frequency 440 Hz electromagnetic radiation which we hear A Yes sound is an electromagnetic wave B No sound is not an electromagnetic wave 1 CAPA 14 Friday Reading 34 8 There is a new and final online participation available Last Maxwell s equations Today More of Maxwell and EM radiation Next More on light and EM radiation 2 Faraday s Law d mag dt And thus Faraday s Law can be written as v v v d v E dl dt B dA Loop surface 3 1 CT 33 14 A long solenoid radius R contains a uniform B field that increases steadily B t c t Consider the dashed Amperian loop What is E dL around the loop going CCW R A zero B 2 rE C 2 RE D r 2 E E R 2 E B r 4 CT 33 14b What is B dA through the the dashed curve A zero B 2 rB C 2 RB D r 2 B E R 2 B R B r 5 CT 33 14c Let s put this together Recall B ct d d Faraday says E dl B dA dt dt Recall the left side is 2 rE 2 Recall B dA r B So how does E depend on r A E constant B E 1 r C E r D E r 2 E Other R B r 6 2 Ampere s Law Maxwell realized that Ampere s Law must be incomplete because he discovered a situation where it gave the wrong answer v v B dl i 0 through 7 B Current i E B Current i 1 As the currents are flowing one has Magnetic Fields around the wires 2 Charge is also building up on the plates creating an increasing Electric Field between them 8 Clicker Question Current i Current i B Consider the Biot Savart Law for Magnetic Fields Is there a Magnetic Field at the point labeled between the plates A Yes there is a B Field B No there is zero B field 9 3 CT 32 10 i dL r v v i dL r dB 0 4 r 2 B 10 Clicker Question Current i Current i B Consider the Biot Savart Law for Magnetic Fields Is there a Magnetic Field at the point labeled between the plates A Yes there is a B Field B No there is zero B field 11 Clicker Question Current i v v B dl i 0 through Current i B Now consider an Amperian Loop as drawn According to Ampere s Law is there a Magnetic Field at the point labeled between the plates Something must be wrong with A Yes there is a B Field Ampere s Law B No there is zero B field 12 4 The changing Electric Field inside the capacitor must act like a current enclosed for Ampere s Law v v B dl 0ienc 0 0 d E dt v v E E dA and 0 d E is often called the Where dt displacement current Thus a changing Electric Field creates a Magnetic Field 13 B Current i E B Current i 14 r v E dA Q r v B dA 0 enclosed r r r r E dl B dl These four equations are called Maxwell s equations 0 These are the axioms of electromagnetism d B dt 0ithrough 0 0 d E dt They are one of the major triumphs of modern science 15 5 Many times you will see the equations in a vector calculus form Oliver Heaviside 16 A shaking charge creates an electromagnetic wave Phet sim Wave self propagating disturbance 1 speed v 4 10 7 N A2 8 85 10 12 F m 1 2 0 0 8 speed v 3 10 m s c Speed of Light 17 Visible Light Example Yellow light Frequency 5E14 Hz 500 nm yellow 18 6 Traveling wave x position T c f c 19 Visible Light 400 nm violet 700 nm red Example 500 nm yellow f c 3x108 550x10 9 5x1014 Hz 20 Television transmissions are in the radio range 1 5 meters f c 108 Hz 100 MHz On Television different channels have different frequencies and thus different wavelengths When you set the channel knob you amplify just that frequency range 21 7
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