Question

In: Physics

Part A How many conduction electrons are there in a 4.50 mm diameter gold wire that...

Part A
How many conduction electrons are there in a 4.50 mm diameter gold wire that is 30.0 cm long?


Part B
How far must the sea of electrons in the wire move to deliver -24.0 nC of charge to an electrode?

Express your answer with the appropriate units.

Solutions

Expert Solution

SOLUTION:
A)

Givens/ conversions:

Diameter ≡ d = 4.50 mm = 0.0045 m
Length ≡ l = 30.0 cm = 0.300 m.

neGOLD = 5.9×1028 m-3

And we need to determine Ne...

Ne = ne⋅V
We can determine volume by V = A⋅l = (π/4)d2⋅l

∴ Ne = ne⋅(π/4)d2⋅l

= (5.9×1028 m-3)(π/4)⋅(0.0045 m)2⋅(0.300 m)

⇒Ne = 2.50101×1026 electrons

-----------------------------------------------------------------------------------------------------
PART B

SOLUTION:
So we know from part A that in 0.3 m, there are 2.50101×1026 electrons ...

....

the desired charge = -24×10-9 C


The total charge created by that many electrons is simply equal to the number of electrons multiplied by the charge or each individual electron, or Qtot = Qe⋅Ne

The charge per unit length can be determined by dividing the total charge by the length from part A.

Q/l = Qe⋅Ne/l = (-1.602×10-19 C)(2.50101×1026)/(0.3 m)
→ Q/l = -1.33553934×108 C/m
lets call this QperLength

The total length (L) required to contain a total charge (Qf) may then be solved for by ... L = Qf/QperLength = l⋅Qf/(Qe⋅Ne)

→ L = (0.2 m)(-24×10-9 C)/[(-1.602×10-19 C)(2.50101×1026)]
⇒ L = 1.19951×10-16 m


Which is a really small number... which brings us to the last aspect. Units... I think that the units (which are units of length, of course) are most likely going to be desired in the same units that the length in part A was expressed, so centimeters...

102 cm/m... so

⇒ L = 1.19951×10-14 cm


Related Solutions

How many conduction electrons are there in a 5.00 mmmm diameter gold wire that is 40.0...
How many conduction electrons are there in a 5.00 mmmm diameter gold wire that is 40.0 cmcm long? How far must the sea of electrons in the wire move to deliver -28.0 nCnC of charge to an electrode?
A current carrying gold wire has diameter of 0.84 mm. the electric field in the wire...
A current carrying gold wire has diameter of 0.84 mm. the electric field in the wire is 0.49 V/m. What is a The current carried by the wire? b The potential difference between two points in the wire 6.4 m apart? c The resistance of a 6.4 m length of this wire.
How much 1.0 mm diameter copper wire would it take to equal the resistance of one...
How much 1.0 mm diameter copper wire would it take to equal the resistance of one 100 Ω resistor? The resistivity of copper is 1.68*10-8 Ωm b) What would be the current if this wire was connected to a 12.0 V battery? c) How many electrons per second pass by a point on the wire? d) If this wire was coiled up and submerged in 100 mL of water at 20oC, how long would it take for the water to...
If the wire diameter decreases to 1 mm but the length is still 20 m and...
If the wire diameter decreases to 1 mm but the length is still 20 m and still carrying the same 20.0 A current, the drift speed of electrons will  (increase / decrease / stay the same), the current density will  (increase / decrease / stay the same), the resistivity of the wire will  (increase / decrease / stay the same), the resistance of the wire will  (increase / decrease / stay the same), the electric field inside the wire will  (increase / decrease / stay...
An electric wire having a diameter of 2.3 mm and covered with a plastic insulation of...
An electric wire having a diameter of 2.3 mm and covered with a plastic insulation of thickness 0.63 mm is exposed to air at 336 K and h= 32W/m2 K. It is assumed that the wire surface temperature is constant at 415 K and is not affected by the covering. Calculate the value of the critical radius. Calculate the heat loss per m of wire length with no insulation and heat loss with insulation being present. Data given: Plastic 0.4...
​How long should a 2.3 mm diameter copper wire be to contain 1024 atoms? Atomic mass...
​How long should a 2.3 mm diameter copper wire be to contain 1024 atoms? Atomic mass and density of Cu are 63.54 g/mol and 8.93 Mg/m3, respectively.
A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the...
A 580-mm long tungsten wire, with a 0.046-mm-diameter circular cross section, is wrapped around in the shape of a coil and used as a filament in an incandescent light bulb. When the light bulb is connected to a battery, a current of 0.526 A is measured through the filament. (Note: tungsten has a resistivity of 4.9 × 10-8 ? • m.) How many electrons pass through this filament in 5 seconds? How many electrons pass through this filament in 5...
A 0.500 mm diameter copper wire makes up a 136 turns, 7.60 cm diameter coil. There...
A 0.500 mm diameter copper wire makes up a 136 turns, 7.60 cm diameter coil. There is a magnetic field parallel to the axis of the coil. If the induced current in the coil is 2.80 A, what is the rate of change of the magnetic field? a) 0.0839 T/s b) 3.63×10-6 T/s c) 12.8 T/s d) 1.74×103 T/s
A helical compression spring is wound using 1 mm-diameter music wire. The outside coil diameter of...
A helical compression spring is wound using 1 mm-diameter music wire. The outside coil diameter of the spring is 11 mm. The ends are squared and there are 12 total turns. (a) Estimate the torsional yield strength of the wire. (b) Estimate the static load corresponding to the yield strength. (c) Estimate the scale of the spring. (d) Estimate the solid length of the spring. (e) Is there any possibility for buckling?
Explain the need for saltatory conduction and how myelination and axon diameter affect rate of conduction...
Explain the need for saltatory conduction and how myelination and axon diameter affect rate of conduction – you can do this as an illustration. Make sure in your answer you include: axon, axon hillock, axon terminal, original action potential, new action potential, Schwann cell, myelin, node of Ranvier, depolarization, refractory DO NOT DEFINE THESE TERMS INDIVIDUALLY please type the answer.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT