Phys 0175 - Lecture 5

# Phys 0175 - Lecture 5 - electric field at P Hence 29 29 29...

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Reminder: Homework Assignment #1: PHYS 0175 – LON-CAPA HW #01 Due on Sunday(@10pm), January 18 th .

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Lecture 5 (Jan. 14, 2009): The electric field due to a circular ring with uniformly distributed net charge The electric field due to a semi-circular ring with uniformly distributed net charge The electric field above the center of a rod with uniformly distributed net charge Chapter 22 (cont’d):
Finding the electric field for a continuous charge distribution instead of for a finite number of point charges: Consider a thin ring of radius R with a uniformly distributed positive net charge Q. Define a linear charge density λ=Q/(2πR). The charge on any segment ds of the ring will then be dq=λ*ds. Such a segment will produce an E field at point P that has magnitude ( 29 2 2 2 kdq k ds dE r z R λ = = +

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From symmetry considerations it follows that the x- and y-components of the electric field at P add to zero when one adds the contributions from all the segments around the ring. On the other hand, every element ds produces the same z-component of the

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Unformatted text preview: electric field at P: Hence ( 29 ( 29 ( 29 1 2 2 2 2 2 2 2 cos cos z k ds k ds z dE dE z R z R z R λ θ = = = + + + ( 29 ( 29 3 3 2 2 2 2 2 2 2 cos R z kz kQz E E dE ds z R z R π = = = = + + ∫ ∫ ( 29 3 2 2 2 z kQz E E z R = = + How does this electric field along the z-axis change with z? What is E at z=0? What is E at z>0? What is E at z<0? What is E at very large values of z? Example 5.1: consider a variation of the previous problem. Shown below is a non-conducting rod that is bent into a half-circle of radius R. It holds a positive net charge Q that is uniformly distributed over the length of the rod. What is the electric field at P? Will E be zero? Will E x be zero? Will E y be zero? x y Example 5.2: A positive net charge Q is distributed uniformly over the length L of a thin non-conducting rod. What is the electric field E at point P located a perpendicular distance R above the rod’s center? Will E be zero? Will E x be zero? Will E y be zero?...
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## This note was uploaded on 04/06/2009 for the course PHYS 0175 taught by Professor Koehler during the Spring '08 term at Pittsburgh.

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Phys 0175 - Lecture 5 - electric field at P Hence 29 29 29...

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