Worksheet: The Magnetic Field due to a Current in a Solenoid

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

Q1:

A length of wire is formed into a solenoid with 𝑛 turns of wire per millimeter. The wire carries a constant current 𝐼. As a result, a magnetic field of strength 𝐡 can be measured at the center of the solenoid. Which of the following changes to the system would increase the magnetic field strength at the center of the solenoid, assuming everything else remains constant?

  • ADecreasing the length of the solenoid by removing turns of wire while keeping 𝑛 constant
  • BDecreasing 𝐼, the current in the wire
  • CDecreasing 𝑛, the number of turns of wire per millimeter
  • DIncreasing 𝐼, the current in the wire
  • EIncreasing the length of the solenoid by adding turns of wire while keeping 𝑛 constant

Q2:

A solenoid is formed of a wire that carries a constant current of 0.16 A. The magnetic field at the center of the solenoid is measured to be 3.8Γ—10οŠͺ T. Calculate the number of turns of wire per cm of the solenoid’s length, rounding to the nearest whole number of turns. Use a value of 4πœ‹Γ—10 Tβ‹…m/A for πœ‡οŠ¦.

Q3:

A wire is given the form of a solenoid S that has 400 turns and a length of 𝑙. The current in S is 𝐼 and the strength of the magnetic field produced by S at its center is 𝐡. A second wire is used to form a solenoid S that has 150 turns. S and S are connected end to end to form a solenoid S. The spacing of the turns of S is adjusted until the length of S is 𝑙 and the turns of S are equidistant from each other. The turns of S are equal in radius to the turns of S. The current in S is 𝐼, and the strength of the magnetic field produced by S at its center is 𝐡. Which of the following describes the relationship between 𝐡 and 𝐡?

  • A𝐡=𝐡
  • B𝐡=811𝐡
  • C𝐡=118𝐡
  • D𝐡=58𝐡
  • E𝐡=83𝐡

Q4:

A solenoid has a length 𝑙 and consists of 𝑁 turns of wire. The wire carries a constant current 𝐼. Which of the following relationships describes the magnetic field strength 𝐡 at the center of the solenoid?

  • Aπ΅βˆπ‘πΌπ‘™
  • Bπ΅βˆπ‘πΌπ‘™οŠ¨
  • Cπ΅βˆπ‘™π‘πΌ
  • Dπ΅βˆπ‘πΌβˆšπ‘™
  • Eπ΅βˆπ‘™π‘πΌοŠ¨

Q5:

A wire that carries a constant current of 0.15 A is formed into a solenoid with 11 turns per centimeter. Calculate the strength of the magnetic field at the center of the solenoid. Give your answer in teslas expressed in scientific notation to one decimal place. Use a value of 4πœ‹Γ—10 Tβ‹…m/A for πœ‡οŠ¦.

  • A1.4Γ—10οŠͺ T
  • B2.1Γ—10οŠͺ T
  • C3.1Γ—10 T
  • D9.2Γ—10 T
  • E3.1Γ—10 T

Q6:

A solenoid is formed of a length of wire which carries a constant current 𝐼. The solenoid has 430 turns of wire per meter. The magnetic field at the center of the solenoid is measured to be 3.2Γ—10 T. Calculate the current, 𝐼, in amperes. Give your answer to 1 decimal place. Use πœ‡=4πœ‹Γ—10β‹…/TmA.

Q7:

A wire that carries a constant current of 0.9 A is formed into a solenoid of length 310 mm. The strength of the magnetic field at the center of the solenoid is measured to be 7.7Γ—10οŠͺ T. Calculate the number of turns used to form the solenoid, giving your answer to the nearest whole number of turns. Use a value of 4πœ‹Γ—10 Tβ‹…m/A for πœ‡οŠ¦.

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