Worksheet: The Torque on a Current-Carrying Rectangular Loop of Wire in a Magnetic Field

In this worksheet, we will practice calculating the torque on a current-carrying rectangular loop of wire in a uniform magnetic field.

Q1:

The diagram shows a rectangular loop of current-carrying wire between the poles of a magnet. The longer sides of the loop are initially parallel to the magnetic field, and the shorter sides of the loop are initially perpendicular to the magnetic field. The loop then rotates through 90∘ so that all its sides are perpendicular to the magnetic field. Which of the lines on the graph correctly represents the change in the torque acting on the loop as the angle its longest sides make with the magnetic field direction varies from 0∘ to 90∘?

  • ABlue
  • BGreen
  • CRed
  • DOrange
  • ENone of these lines

Q2:

The diagram shows a rectangular conducting coil with 5 turns that is in a magnetic field with a strength of 650 mT. The sides of the loop parallel to line 𝑑 are parallel to the magnetic field, and the sides of the loop parallel to line 𝑑 are perpendicular to the magnetic field. The length of 𝑑=0.055m and the length of 𝑑=0.035m. The torque on the loop is 1.2 mN⋅m. What is the current in the loop? Answer to the nearest milliampere.

Q3:

The diagram represents a rectangular loop of wire at three different rotational positions in a uniform magnetic field. The wire loop carries a constant current supplied from an external circuit that is not shown in the diagram.

Which color arrows correctly represent the variation in the magnetic force on the loop as it rotates?

  • AThe black arrows
  • BThe blue arrows

Which color arrows correctly represent the variation in the magnetic dipole moment of the loop as it rotates?

  • AThe blue arrows
  • BThe black arrows

Q4:

The diagram shows a rectangular conducting coil with 4 turns that is in a magnetic field with a strength of 325 mT. There is a current of 4.8 A in the coil. The sides of the loop parallel to line 𝑑 are parallel to the magnetic field, and the sides of the loop parallel to line 𝑑 are perpendicular to the magnetic field. The ratio of 𝑑 to 𝑑 is 1.5. The torque on the loop is 12.5 mN⋅m. Find the length of 𝑑 to the nearest millimeter.

Q5:

Which of the following formulas correctly describes the relation of 𝑚, the magnetic dipole of a loop of current-carrying wire in a uniform magnetic field, to 𝜏, the torque acting on the loop, and 𝐵, the magnitude of the magnetic field?

  • A𝑚=𝐵+𝜏
  • B𝑚=𝐵𝜏𝐵+𝜏
  • C𝑚=𝐵𝜏
  • D𝑚=𝐵𝜏
  • E𝑚=𝜏𝐵

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