Ch – 28 Current and Conductivity
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Transcript of Ch – 28 Current and Conductivity
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Ch – 28 Current and Conductivity
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Current: Motion of charge through a conductor
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How do we know there is a current?
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Charge carriers• 18th century: Franklin and others developed the single
fluid theory of electricity. Electricity flows from a body with an excess of charge (positive) to one with a deficit of charge (negative).
• Theories of electricity advanced with the assumption of a positive charge carrier.
• 19th century: Thompson and others suggested that negatively-charged electrons were the charge carriers, in a conductor.
• Confirmed by Tolson and Stewart in 1916• Most engineering applications still assume positive
charge carriers (aka electron holes)
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Electron Current (aka actual current)
• Sea of electrons move randomly but net motion=0 when conductor is in equilibrium
• a force due to the presence of an external E field will cause the sea of electrons to move with vd - drift velocity
Moving sea of electrons
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Electron Current
• The number of electrons per second that pass through a cross sectional area of wire or other conductor:
i = Ne/∆t
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Electron current, cont’dNe (number of electrons) = i ∆tNe = nV where V is the volume of the wire (A ∆x) and n is the
conduction electron density (on the order of 1028 electrons per m3)∆x = vd ∆t, therefore:
Ne = nAvd ∆tNe/∆t = i = nAvd
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Stop to think
• These four wires are made of the same metal. Rank, in order, from largest to smallest, the electron currents ia to id
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Answer: c,b,a,d
i is proportional to r2vd. Changing r has more influence than changing v by the same amount
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Numerical Problem
1.0 x 1016 electrons flow through a x-section of silver wire in 320 μs with a drift velocity of 8.0 x 10 -4 m/s. What is the diameter of the wire?
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Answer
9.26 x 10-4 m
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Conservation of Current• The drift velocity of
electrons is the same throughout the wire
• The electrons themselves can’t go anywhere while traveling through the wire
• Therefore the current going in is equal to the current coming out
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Creating a current
An electron current is a non-equilibrium motion of charges sustained by an electric field
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E field in a wire
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E field in a wire• On-axis field for charged ring
– points away from positive charge, towards ring for negative charge
– is proportional to the charge on the ring– decreases with distance from the ring
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Stop to think# 2, page 886 in text
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Answer
d>b>e>a=cE depends on the difference in the charge
on the two rings. The E fields of a and c are zero. The difference is the greatest for
the rings of d.
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Problem
• What is the surface charge density of a 1.0 mm-diameter wire with 1000 excess electrons per cm of length?
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Answer
ή = 5.1 x 10-12 C/m2
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Conventional Current
• The rate in coulombs per second, at which charge moves in the direction of E– For constant current I = ∆Q/∆t – For changing current I = dQ/dt
• Current direction from positive terminal to negative terminal, opposite the direction of electrons in a metal
• I = ∆Q/∆t = -(eNe/ ∆t) = -ei (sign for direction)
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Problem- constant current
In an ionic solution, 5.0 x 1015 positive ions with charge +2e pass to the right, while 6.0 x 1015 negative ions with charge –e pass to the left. What is the current in the solution and what is the direction of the E field?
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Answer –constant current
2.56 mA (milliamps). E field is to the right
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Problem – changing current
The current in a wire at time t is given by the expression: I = (2.0 A)e-t/(2.0μs) where t is in μs and t>=0.
a. Graph I vs t for 0<=t<=10 μs (2 μs intervals)b. Find an expression for the total amount of
charge that is entering the wire at time t. Q=0C at t=0 μs.
c. Graph Q vs t for 0<=t<=10 μs (2 μs intervals).
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Answer – changing current
a. See top graph
b. Q = (4.0 μC)[1- e-t/(2.0μs)]
c. See bottom graph
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Current Density in a Wire
• I = ei = nevd A• Define current density as :
J = I/A = nevd (A/m2)• This quantity is not the same as surface
charge density, which implies electrostatic conditions (no moving charge)
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Current Density Conceptual Questions
The current in wire is doubled. By what factor do the following change?
a. Current densityb. Conduction-electron densityc. Electron drift speed
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Current Density Conceptual Answers
A. J increases by a factor of 2 (J = I/A)B. n remains the same (property of the
metal)C. vd increases by a factor of 2 (J = nevd)
and e is the charge on the electron, which is constant.