PHYS1322-CH22Lec1

PHYS1322-CH22Lec1 - Lecture 4 Lecture 4 What is a Field? A...

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Lecture 4 Lecture 4 What is a Field? ± A FIELD is something that can be defined anywhere in space ± It is a mathematical concept that represents a physical property •It can be a scalar field (e.g., Temperature field) •Only a magnitude is defined •It can be a vector field (e.g., Electric field) •Has a magnitude AND direction 77 82 83 68 55 66 83 75 80 90 91 75 71 80 72 84 73 82 88 92 77 88 88 73 64 Temperature Field These isolated temperatures sample the scalar field (you only learn the temperature at the point you choose, but T is defined everywhere ( x , y ) ) 77 82 83 68 55 66 83 75 80 90 91 75 71 80 72 84 73 57 88 92 77 56 88 73 64 A Vector Field You may want to know which way the wind is blowing. .. That would require a vector field (you learn both wind speed and direction) The Electric Field Note: The net Coulomb force on a given charge is always proportional to the strength of that charge. q q 1 q 2 F 1 F F 2 test charge 12 11 2 2 22 01 2 ˆˆ 4 FFF qr q F rr πε =+    GGG G •We can now define a quantity, the electric field , which is independent of the test charge, q , and depends only on position of q in space and the charges producing the field: The q i are the sources of the electric field F E q G G 2 0 ˆ 1 4 ii i i E r = G –Note +ve charge produces field pointing away from the charge -- -ve charge produces field pointing towards the charge The Electric Field With this concept, we can “map” the electric field anywhere in space produced by any arbitrary: Field E at this point + F These charges or this charge distribution “source” the electric field throughout space 2 0 1 ˆ 4 i i i q E r r = G + + + + + + - - - - - Bunch of Charges 2 0 1 ˆ 4 dq E r r = G + + + + + ++ + + + + Charge Distribution F E q G G
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Lecture 4 Example: Electric Field The x and y components of the field at (0,0) are: 1) Notice that the fields from the top-right and bottom left cancel at the origin?
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PHYS1322-CH22Lec1 - Lecture 4 Lecture 4 What is a Field? A...

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