Prozorov_02 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURE 2 Electric field and forces. Superposition. Dipole. a concept of fields scalar (single valued) – temperature distribution field Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 2 vector field: a wind map magnitude and direction Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 3 field lines – follow the same magnitude Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 4 schematic view of an electric field Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 5 more formal definition Q1Q2 r Fk 2 r r - Coulomb law we can re-write this as: Q1Q2 r Q1 r Fk 2 k 2 Q2 EQ2 r r r r here E represents an electric field created by charge Q1 at the location of charge Q2. Note, that this field does not depend on Q2, so it is fully determined by the charge Q1. Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 6 properties of an electric field • An electric field is a vector field that surrounds electric charges. This electric field exerts a force on other charges. Michael Faraday introduced the concept of an electric field. • The electric field is a vector field with SI units of [N/C] or, equivalently, [V/m]. The SI base units of the electric field are [kg·m/(s3·A)]. • The strength or magnitude of the field at a given point is defined as the force that would be exerted on a positive test charge of 1 C placed at that point • The direction of the field is given by the direction of that force. Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 7 why is it useful? • because we can first calculate the total electric field for arbitrary distribution of charges (even continuous) and then forget about them. • Once the electric field is known at any point in space, we can compute all electrostatic properties for a “test” charge, q, placed anywhere. For example, the force will be: F r qE r Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 8 charge density • an electric field is most useful to represent extended charged bodies • we have learned the Coulomb’s law for two pointlike charges • what about a charged rod? what is the force of that rod on a charge q? q Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 9 linear charge density total charge of the rod is Q Q C linear charge density is: L m length L ab b Q dx b a L a Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 10 let’s think of small segments due to superposition principle, each segment contributes electric field: dQ dEx k 2 cos r dQ dE y k 2 sin r Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 11 r 2 r 2 x2 y 2 x cos r y sin r dEx k dE y k dy a total electric field is then: Ex k a x 2 dy a Ey k a x y 2 2 y 2 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 3/2 3/2 dQ x2 y 2 3/2 dQ x 2 y 2 3/2 x y x y 24 August 2011 12 these integrals are easy to take (or look up in the tables): a a dy x 2 y 2 3/2 a 2a x 2 a x 2 2 a ydy x 2 y 2 3/2 0 2k a a Ex 2 2 2 0 x a 2 x 2 x a x Ey 0 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 13 an infinite rod Suppose that the rod is very, very long. Then a 1 Ex lim 2 2 a 2 2 0 x 0 x a x Ey 0 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 14 a charged plane similarly, for a charged plate of area S we introduce surface charge density: Q S C m2 if the plate is infinite, an electric field has only perpendicular to the plate component: Ex 2 0 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 15 two oppositely charged planes electric field is confined to the space between the plates Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 16 two charged plates: an experiment Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 17 electron in a uniform field y + x remember 221? E 2 0 F eE e ˆ a y m m 0m - field of infinite charged plane (there is no “2” in the denominator) how does this motion look in x-y coordinates? Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 18 velocity along x-axis does not change (no force) x v0t , so t x v0 along y-axis: t2 e 2 ya t 2 2 0 m eliminating t we obtain: x2 e ya 2 x2 2 2v0 2 0 mv0 so, it is a parabola! Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 19 electric field lines (vs vectors) Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 20 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 21 Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 22 an electric dipole Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 23 water molecule Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 24 electric dipole moment and its field 2 d y 2 1 1 E y E y , E y , kq 2 2 q d d k y y 2 2 2 d y 2 E y , k E y , q if d << y, then 2kqd p Ey 3 , p qd 3 y 2 0 y in general: in the above example: p r r E 3 p 3 2 4 0 r r 1 p 0, qd 1 dqy 2 dq 3 2 qd E 3 4 0 y y 2 0 y 3 r 0, y Physics 222 - Prof. Ruslan Prozorov - Iowa State University 24 August 2011 25 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.

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