Chapter 24c - Chapter 24: Electric Potential Part C ! ! ! !...

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September 18, 2009 Ch. 24: Electric Potential - Part C 1 Chapter 24: Electric Potential – Part C ! Review of electric potential. ! HITT question. ! Calculating the field from the potential. ! Electric potential energy of a system of point charges. ! HITT question ! Potential of a charged isolated conductor.
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September 18, 2009 Ch. 24: Electric Potential - Part C 2 Electric Potential ! The electric potential V is the potential energy per unit charge at a point in an electric field. U V q = ! Calculating the electric potential from the field. f fi i VV E d s −= ! ! ! Potential due to a point charge. 0 1 4 q V r πε =
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September 18, 2009 Ch. 24: Electric Potential - Part C 3 Electric Potential ! Potential due to a group of point charges. ! Potential due to an electric dipole. ! Potential due to a continuous charge distribution. 11 0 1 4 nn i i i q VV r πε == ∑∑ 2 0 1 4 cos p V r θ = 0 1 4 dq dV r = 0 1 4 dq Vd V r ∫∫ and
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September 18, 2009 Ch. 24: Electric Potential - Part C 4 Electric Potential ! Electric potential due to a line of charge. 22 0 4 ln LL d V d λ πε  ++ =   ! Electric potential due to a charged disk. ( ) 0 2 Vz R z σ ε =+ () ( ) 0 0 2 1 4 '' ' R Rd R V zR σπ = + 0 0 1 4 L dx V xd = +
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September 18, 2009 Ch. 24: Electric Potential - Part C 5 HITT Question A) -4kq/d ; B) -2kq/d; C) -4kq/2 1/2 d; D) +4kq/d; E) 0. In the figure 8 particles form a square with a distance d between adjacent particles. What is the electric potential at point P at the center of the square?
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September 18, 2009 Ch. 24: Electric Potential - Part C 6 Calculating the Field from the Potential 0 dW dU q dV =− ! Consider a family of closely spaced equipotential surfaces, with a potential difference between each pair of adjacent surfaces of dV . ! At any point P the electric field E is perpendicular to the equipotential surface through P. ! Let a positive test charge q 0 move through a displacement ds from one equipotential surface to the adjacent surface. The work done by the electric field during the move is: 00 (cos ) d WF d sq E d E d s θ =⋅ = = !!
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September 18, 2009 Ch. 24: Electric Potential - Part C 7 Calculating the Field from the Potential 00 (cos ) qdV qE d s θ −= (cos ) dV E ds =− However, is the component of the electric field E in the direction of ds ; therefore cos E s V E s ; ; .
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Chapter 24c - Chapter 24: Electric Potential Part C ! ! ! !...

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