Worksheet: Current Density

In this worksheet, we will practice describing current density as a vector determining the electric current through an area perpendicular to the current direction.

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=8.48×10 electron/m3.

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

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

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

  • A 5 . 1 7 × 1 0   m/s
  • B 5 . 4 1 × 1 0   m/s
  • C 5 . 6 0 × 1 0   m/s
  • D 5 . 8 0 × 1 0   m/s
  • E 4 . 8 2 × 1 0   m/s

Q2:

An electron beam with a radius of 0.90 mm has a measured current 𝐼=30.00μA. What is the magnitude of the current density of the beam?

Q3:

A high-energy proton accelerator produces a proton beam with a radius 𝑟=0.73 mm. The constant beam current 𝐼=5.0 μA. The beam’s charge density 𝑛=3.7×10 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 2 . 5 × 1 0  m/s
  • B 1 . 3 × 1 0  m/s
  • C 5 . 0 × 1 0  m/s
  • D 7 . 5 × 1 0  m/s
  • E 6 . 8 × 1 0  m/s

How much time is required for 2.3×10 protons to be emitted by the accelerator?

Q4:

A wire has a circular cross-section with a radius 𝑅=3.000 mm. The current density in the wire is non-uniform and is modeled as 𝐽=𝑐𝑟, where 𝑐 is a constant with units of Am/. The magnitude of 𝐽 is 5.00×10/𝑟Am. What magnitude of current is carried by the inner section of the wire from the axis to 𝑟=0.50𝑅?

Q5:

A cylindrical wire with radius 𝑅=0.50mm has a current density 𝐽=𝐽𝑅𝑟, where 𝐽=16,000/Am. What is the current through the wire?

Q6:

A rod has a square cross section with sides of length 2.0 cm. The current density in the rod 𝐽=𝐽𝑒kk=0.50⋅𝑒Am×, where 𝑥 is measured in meters, as shown in the diagram. Find the current through the face of the rod.

Q7:

A 20 gauge wire has a cross-sectional area of 0.518 mm2. The current in the wire is modeled as 𝐼(𝑡)=2.00×(80𝜋𝑡)sin, where 𝑡 is measured in seconds. What is the current density in the wire at the instant 𝑡=10.00ms?

  • A 7 3 . 4 × 1 0  A/m2
  • B 1 5 . 5 × 1 0  A/m2
  • C 2 7 . 8 × 1 0  A/m2
  • D 8 1 . 2 × 1 0  A/m2
  • E 2 . 2 7 × 1 0  A/m2

Q8:

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 6 . 5 7 × 1 0   cm−3
  • B 6 . 5 0 × 1 0   cm−3
  • C 7 . 1 3 × 1 0   cm−3
  • D 3 . 1 7 × 1 0   cm−3
  • E 3 . 5 7 × 1 0   cm−3

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