Worksheet: The Magnetic Field due to a Current in a Circular Loop of Wire

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

Q1:

A circular loop of wire is carrying a constant current 𝐼 in a clockwise direction as viewed from above. The current creates a magnetic field. Based on the diagram, state the direction of the magnetic field at the center of the coil.

  • A
  • B
  • C
  • D

Q2:

A circular loop of wire of radius 50 mm carries a constant current 𝐼 A and produces a magnetic field of strength 𝐵 T at its center. Another circular loop of wire has a radius of 150 mm. Given that this wire also carries a constant current of 𝐼 A, which of the following correctly shows the relation between 𝐵, the strength of the magnetic field produced by the larger loop, and 𝐵?

  • A𝐵=𝐵
  • B𝐵=3𝐵
  • C𝐵=13𝐵
  • D𝐵=9𝐵
  • E𝐵=19𝐵

Q3:

A circular loop of wire carries a constant current of 0.9 A. The radius of the loop is 13 mm. Calculate the strength of the magnetic field at the center of the loop. Give your answer in teslas expressed in scientific notation to 1 decimal place. Use a value of 4𝜋×10 T⋅m/A for 𝜇.

  • A3.3×10 T
  • B1.4×10 T
  • C8.7×10 T
  • D3.5×10 T
  • E4.3×10 T

Q4:

A circular loop of wire with a radius of 9.5 cm carries a constant current of 𝐼 A. The strength of the magnetic field produced by the current is 5.2×10 T at the center of the loop. Calculate 𝐼, rounding your answer to 1 decimal place. Use a value of 4𝜋×10 T⋅m/A for 𝜇.

Q5:

A thin, circular coil of wire with a radius of 22 mm that has 𝑁 turns carries a constant current of 0.45 A. The strength of the magnetic field produced by the current is 2.3×10 T at the center of the coil. Calculate 𝑁 to the nearest whole number of turns. Use a value of 4𝜋×10 T⋅m/A for 𝜇.

Q6:

A thin, circular coil of wire with a radius of 2.3 cm has 28 turns. The coil carries a constant current of 330 mA. The strength of the magnetic field produced is measured to be 𝐵 T at the center of the coil. After the measurement of the magenetic field, the coil is reshaped so that it has the same length but 6 fewer turns of wire. The current in the coil is then adjusted until the strength of the magnetic field produced at the center of the coil is 𝐵 T. Calculate the new value of the current. Give your answer in milliamperes to the nearest whole number. Use a value of 4𝜋×10 T⋅m/A for 𝜇.

Q7:

A thin, circular coil of wire with radius 𝑟 and 𝑁 turns carries a constant current. The strength of the magnetic field at the center of the coil is measured to be 2.3×10 T. Some time later, 2𝑁 turns of wire are added to the coil. The current passing through the coil remains the same. Calculate the strength of the magnetic field at the center of the coil after the loops of wire are added. Give your answer in teslas expressed in scientific notation to 1 decimal place.

  • A4.6×10 T
  • B4.3×10 T
  • C1.2×10 T
  • D2.3×10 T
  • E6.9×10 T

Q8:

A circular loop of wire with a radius of 𝑟 mm carries a constant current of 2.1 A. The strength of the magnetic field produced is 1.7×10 T at the center of the loop. Calculate 𝑟, giving your answer in millimeters to 1 decimal place. Use a value of 4𝜋×10 T⋅m/A for 𝜇.

Q9:

A circular loop of wire is carrying a constant current 𝐼 that induces a magnetic field. The loop intersects a flat plane at points 𝑃 and 𝑅. The wire is normal to the plane at the points of intersection. A small compass is placed in the plane at the center of the loop of wire, 𝑄, with its face pointing upward. In which direction will the needle of the compass point?

  • A
  • B
  • C
  • D

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