# 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 electron/m3.

Find the magnitude of current density in the air conditionerβs wiring.

• A A/m2
• B A/m2
• C A/m2
• D A/m2
• E A/m2

Find the magnitude of the drift velocity in the air conditionerβs wiring.

• A m/s
• B m/s
• C m/s
• D m/s
• E m/s

Q2:

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

Q3:

A high-energy proton accelerator produces a proton beam with a radius mm. The constant beam current ΞΌA. The beamβs charge density 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 m/s
• B m/s
• C m/s
• D m/s
• E m/s

How much time is required for protons to be emitted by the accelerator?

Q4:

A wire has a circular cross-section with a radius mm. The current density in the wire is non-uniform and is modeled as , where is a constant with units of . The magnitude of is . What magnitude of current is carried by the inner section of the wire from the axis to ?

Q5:

A cylindrical wire with radius has a current density , where . 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 , where 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 , where is measured in seconds. What is the current density in the wire at the instant ?

• A A/m2
• B A/m2
• C A/m2
• D A/m2
• E 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 cmβ3
• B cmβ3
• C cmβ3
• D cmβ3
• E cmβ3