lecture24

# lecture24 - MATH 100 Lecture 24 Applications University...

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2006 Fall MATH 100 Lecture 8 1 MATH 100 Lecture 24 Applications z University gravity: particles with mass m and M attract each other with force z The magnitude of the force z We call fields of such a kind inverse-square field . 3 () GmM F rr r =− K K K 3 GmM F r K K K

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2006 Fall MATH 100 Lecture 8 2 z Coulomb’s law: the electrostatic force exerted by one charged particle on another is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. 3 0 () 4 qQ F rr r πε = K K K
2006 Fall MATH 100 Lecture 8 3 Conservative field z Both gravity field and electrostatic fields are conservative: z Proof: 22 2 (,,) c xyz x yz φ = + + () 3/2 222 ij k xx x cx cy cz k Fr φφ ∂∂ ∇= + + =++ ++ = K KK K K K

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2006 Fall MATH 100 Lecture 8 4 MATH 100 Lecture 24 Application Flow field (,,) steady flow field since no time dependence : oriented surface in a flow field, then component of on normal direction Net vol. of fluid Fx y z f x yzi g x y z j hx yzk Fn F σ =++ ⋅− G G GG G crossing in a unit of time
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lecture24 - MATH 100 Lecture 24 Applications University...

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