p240_ct4_f07

p240_ct4_f07 - Physics 240 Fall 2007 Lecture#4 Dr Dave Winn...

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Unformatted text preview: Physics 240 Fall 2007 Lecture #4 Dr. Dave Winn 2405 Randall Lab [email protected] Electric and Gravitational Field • Electric field defined by: • Same idea used for gravitational field: • In both cases, this idea of the field eliminates the need for action-at-a- distance. • Electric (gravitational) forces are local interactions between charges (masses) and electric (gravitational) fields • This ‘field’ concept is central to modern physics. test test Q F E K G = test test m F g K G = E Field due to a point charge • What is the quantitative electric field due to a positive point charge? • Points everywhere away from the charge, falls off with distance r r kQ r r kQQ Q Q F E test test test test ˆ ˆ 1 2 2 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = = K G E Field due to a dipole Field at each point is the vector sum of the field from the positive charge and the negative charge: − + + = E E E G G G E + E- Dipole field along axis • Calculate field at point P • Reducing this with algebra given in the book we find: • The quantity q*d is called the “dipole moment” p of the dipole. 2 2 − + − = r kq r kq E ) ( 2 2 3 2 qd z k z d z kq E alongaxis = = 3 2 z kp E alongaxis = General methods for calculating fields from charge distributions To find the total field from a distribution of charge: 1. Find a simple way to break the object up into little elements of charge dq (charge/unit length λ , charge/unit area σ , charge/unit volume ρ ) 2. Express the field d E from each little piece of charge....
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p240_ct4_f07 - Physics 240 Fall 2007 Lecture#4 Dr Dave Winn...

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