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Worksheet: Current Density

Q1:

The current supplied to an air conditioner unit is 4.00 A. The air conditioner is wired using a 10-gauge (diameter 2.588 mm) wire. The charge density in the wire is 𝑛 = 8 . 4 8 Γ— 1 0 2 8 electron/m3.

Find the magnitude of current density in the air conditioner’s wiring.

  • A 8 . 0 0 Γ— 1 0 5 A/m2
  • B 7 . 8 8 Γ— 1 0 5 A/m2
  • C 8 . 2 1 Γ— 1 0 5 A/m2
  • D 7 . 6 0 Γ— 1 0 5 A/m2
  • E 8 . 3 5 Γ— 1 0 5 A/m2

Find the magnitude of the drift velocity in the air conditioner’s wiring.

  • A 5 . 6 0 Γ— 1 0 βˆ’ 5 m/s
  • B 5 . 4 1 Γ— 1 0 βˆ’ 5 m/s
  • C 5 . 1 7 Γ— 1 0 βˆ’ 5 m/s
  • D 4 . 8 2 Γ— 1 0 βˆ’ 5 m/s
  • E 5 . 8 0 Γ— 1 0 βˆ’ 5 m/s

Q2:

An electron beam with a radius of 0.90 mm has a measured current 𝐼 = 3 0 . 0 0 μ A . What is the magnitude of the current density of the beam?

Q3:

A high-energy proton accelerator produces a proton beam with a radius π‘Ÿ = 0 . 7 3 mm. The constant beam current 𝐼 = 5 . 0 ΞΌA. The beam’s charge density 𝑛 = 3 . 7 Γ— 1 0 1 1 protons/m3.

What is the magnitude of the current density of the beam?

What is the magnitude of the drift velocity of the beam?

  • A 5 . 0 Γ— 1 0 7 m/s
  • B 1 . 3 Γ— 1 0 7 m/s
  • C 7 . 5 Γ— 1 0 7 m/s
  • D 2 . 5 Γ— 1 0 7 m/s
  • E 6 . 8 Γ— 1 0 7 m/s

How much time is required for 2 . 3 Γ— 1 0 1 0 protons to be emitted by the accelerator?

Q4:

A cylindrical wire with radius 𝑅 = 0 . 5 0 m m has a current density 𝐽 = ο€½ 𝐽 𝑅  π‘Ÿ 0 , where 𝐽 = 1 6 0 0 0 / 0 2 A m . What is the current through the wire?

Q5:

A wire has a circular cross-section with a radius 𝑅 = 3 . 0 0 0 mm. The current density in the wire is non-uniform and is modeled as 𝐽 = 𝑐 π‘Ÿ 2 , where 𝑐 is a constant with units of A m / 4 . The magnitude of 𝐽 is 5 . 0 0 Γ— 1 0 / π‘Ÿ 6 4 2 A m . What magnitude of current is carried by the inner section of the wire from the axis to π‘Ÿ = 0 . 5 0 𝑅 ?

Q6:

A 20 gauge wire has a cross-sectional area of 0.518 mm2. The current in the wire is modeled as 𝐼 ( 𝑑 ) = 2 . 0 0 Γ— ( 8 0 πœ‹ 𝑑 ) s i n , where 𝑑 is measured in seconds. What is the current density in the wire at the instant 𝑑 = 1 0 . 0 0 m s ?

  • A 8 1 . 2 Γ— 1 0 3 A/m2
  • B 3 3 . 2 Γ— 1 0 3 A/m2
  • C 7 3 . 4 Γ— 1 0 3 A/m2
  • D 2 7 . 8 Γ— 1 0 3 A/m2
  • E 1 5 . 5 Γ— 1 0 3 A/m2

Q7:

If there is one free electron per atom of zinc, find its electron number density. Use a value of 7.13 g/cm3 for the density of zinc.

  • A 3 . 5 7 Γ— 1 0 2 2 cmβˆ’3
  • B 7 . 1 3 Γ— 1 0 2 2 cmβˆ’3
  • C 6 . 5 0 Γ— 1 0 2 2 cmβˆ’3
  • D 6 . 5 7 Γ— 1 0 2 2 cmβˆ’3
  • E 3 . 1 7 Γ— 1 0 2 2 cmβˆ’3

Q8:

A rod has a square cross section with sides of length 2.0 cm. The current density in the rod 𝐽 = 𝐽 𝑒 π‘œ 𝛼 π‘₯ k k = ο€Ή 0 . 5 0 β‹…  𝑒 A m 2 ( 2 . 1 Γ— 1 0 ) π‘₯ βˆ’ 3 , where π‘₯ is measured in meters, as shown in the diagram. Find the current through the face of the rod.