Lecture_10

# Lecture_10 - Example Different Paths near Point Charge 1...

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1. Along straight radial path: E = 1 4 πε 0 q r 2 ˆ r r i r f = Δ f i l d E V = Δ f i r r dr r q V 2 0 1 4 1 πε f i r r r q V = Δ 1 4 1 0 πε i f i f V V r r q V = = Δ 1 1 4 1 0 πε + q Example: Different Paths near Point Charge Δ V = 1 4 πε 0 q r 2 ˆ r dr r i r f

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r q V 1 0 4 1 πε = r →∞ , V=0 Negative charge Positive charge V at Infinity
What is E inside metal? E = 0 Δ V = V f V i = E d l i f What is the potential difference ( V f – V i ) ? 0 = Δ V Is V zero everywhere inside a metal? No! But it is constant In static equilibrium Potential Difference in Metal In static equilibrium the electric field is zero at all locations along any path through a metal. Δ V = E x Δ x + E y Δ y + E z Δ z ( ) The potential difference is zero between any two locations inside the metal, and the potential at any location must be the same as the potential at any other location. i f

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E d = 3 mm +Q -Q E Q / A ε 0 Δ V = E d l i f E = (6 Volts)/(0.003 m) = 2000 Volts/m Δ V = 6 Volt +3 V -3 V Charges are on surface Potential in Metal In static equilibrium A Capacitor with large plates and a small gap of 3 mm has a potential difference of 6 Volts from one plate to the other. Δ V = Ed = 6 V
d = 3 mm +Q 1 -Q 1 1 mm 0 1 1 / ε A Q E Charges +Q 2 and Q 2 0 2 2 / ε A Q E What are the charges Q 1 and Q 2 ? Now we have 2 capacitors instead of one Δ V = E d l i f Δ V left = Δ V right = 2000 V/m ( ) 0.001 m ( ) = 2 V Δ V = 4 V There is no “ conservation of potential” ! Potential in Metal In static equilibrium Insert a 1 mm thick metal slab into the center of the capacitor.

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