Worksheet: The Magnetic Field due to a Current in a Straight Wire

In this worksheet, we will practice calculating the magnetic field produced by a current in a straight wire.

Q1:

The diagram shows a long straight wire that carries a current 𝐼. As a result, a magnetic field that is far stronger than Earth’s magnetic field can be measured at point 𝑃, which is a short distance away from the wire. If a small compass is placed at point 𝑃, with its face pointing in the opposite direction to the current, which direction will the needle point?

  • A
  • B
  • C
  • D

Q2:

A long, straight wire is carrying a constant current 𝐼 that induces a magnetic field 𝐡. Magnetic field lines of 𝐡 are shown in the diagram. Based on the diagram, state the direction of the conventional current in the wire.

  • AThere is no current in the wire.
  • BBottom to top
  • CTop to bottom

Q3:

Which of the following correctly describes the relationship between 𝐡, π‘Ÿ, and 𝐼, where 𝐡 is the magnetic field strength measured at a perpendicular distance π‘Ÿ away from a long straight wire carrying a constant current of 𝐼?

  • Aπ΅βˆπΌπ‘ŸοŠ¨
  • Bπ΅βˆπ‘ŸπΌοŠ¨
  • Cπ΅βˆπΌπ‘Ÿ
  • Dπ΅βˆπΌβˆšπ‘Ÿ
  • Eπ΅βˆπ‘ŸπΌ

Q4:

A long, straight wire is carrying a direct current, which produces a magnetic field of strength 𝐡 teslas at a perpendicular distance of 𝑑 cm from the wire. Assuming the system does not change, what is the relationship between 𝐡 and the strength of the magnetic field strength 𝐡 at a perpendicular distance of 2𝑑 cm from the wire? Assume 𝐡 and 𝐡 are much greater than the magnetic field strength of Earth.

  • A𝐡=𝐡
  • B𝐡=2𝐡
  • C𝐡=14𝐡
  • D𝐡=12𝐡
  • E𝐡=4𝐡

Q5:

A magnetic field of strength 10Γ—10 T is measured at a perpendicular distance of 12 cm from a long, straight wire. Some time later, a magnetic field strength of 20Γ—10 T is measured at a perpendicular distance of 6 cm from the same wire. Assuming no other changes to the system, which of the following statements describes the magnitude of the current being carried by the wire between the two measurements?

  • AThe current being carried by the wire remains the same between the first and second measurements.
  • BThe current being carried by the wire decreases between the first and second measurements.
  • CThe current being carried by the wire increases between the first and second measurements.

Q6:

A straight wire in an electrical circuit carries a direct current of 𝐼 A. The resulting magnetic field at a perpendicular distance of 18 mm from this wire is measured to be 1.2Γ—10οŠͺ T. Calculate 𝐼 to the nearest ampere. Use 4πœ‹Γ—10 Tβ‹…m/A for the value of πœ‡οŠ¦.

Q7:

A long wire is carrying a direct current. As a result, a magnetic field of 8.0Γ—10 T can be measured at a perpendicular distance of 13 cm from the wire. What would the strength of the magnetic field be at a perpendicular distance of 26 cm from the wire? Give your answer in scientific notation to one decimal place.

  • A4.0Γ—10 T
  • B2.7Γ—10 T
  • C3.2Γ—10οŠͺ T
  • D1.6Γ—10οŠͺ T
  • E2.0Γ—10 T

Q8:

A long, straight cable in an industrial power plant carries a direct current of 100 A. Calculate the strength of the resulting magnetic field at a perpendicular distance of 0.06 m from this cable. Use 4πœ‹Γ—10 Tβ‹…m/A for the value of πœ‡οŠ¦. Give your answer in scientific notation to two decimal places.

  • A1.67Γ—10 T
  • B5.56Γ—10 T
  • C3.33Γ—10οŠͺ T
  • D3.00Γ—10 T
  • E2.10Γ—10 T

Q9:

A long, straight wire is carrying a constant current 𝐼 that induces a magnetic field 𝐡. Which of the following diagrams most accurately represents magnetic field lines of 𝐡?

  • A
  • B
  • C
  • D
  • E

Q10:

The diagram shows a long, straight, horizontal wire that carries a current 𝐼. As a result of the current, a magnetic field is produced, which is measured at point 𝑃. The point 𝑃 is in the plane of the wire, a short perpendicular distance from the wire. What is the direction of the magnetic field at point 𝑃?

  • A
  • B
  • C
  • D

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