This lesson includes 23 additional questions and 24 additional question variations for subscribers.

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

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 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 to ?

- 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 are parallel to the magnetic field, and the sides of the loop parallel to line are perpendicular to the magnetic field. The length of and the length of . 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 are parallel to the magnetic field, and the sides of the loop parallel to line are perpendicular to the magnetic field. The ratio of to is 1.5. The torque on the loop is 12.5 mN⋅m. Find the length of to the nearest millimeter.

**Q6: **

The diagram shows a rectangular loop of current-carrying wire between the poles of a magnet. The sections of the loop ab and dc are perpendicular to the magnetic field. The diagonal lines bc and ad are aligned at an angle from the direction of the magnetic field. The current in the loop is 1.75 A, and the magnetic field strength is 0.15 T. Length and length . Find the torque acting on the loop to the nearest micronewton-meter.

**Q7: **

The diagram shows a rectangular loop of current-carrying wire between the poles of a magnet that produces a field with a magnitude of 250 mT. 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 has a magnetic dipole moment of 500 μN⋅m/T. The loop is then rotated through so that all its sides are perpendicular to the magnetic field.

How much does the torque on the loop change by due to its rotation? Answer to the nearest micronewton-meter.

**Q8: **

The diagram shows a rectangular conducting coil with 3 turns that is in a magnetic field. There is a current of 8.5 A in the coil. The sides of the loop parallel to line are parallel to the magnetic field, and the sides of the loop parallel to line are perpendicular to the magnetic field. The length of and the length of . The torque on the loop is 15 mN⋅m. Find the magnitude of the magnetic field to the nearest millitesla.

**Q9: **

The diagram shows a rectangular loop of current-carrying wire between the poles of a magnet. The sides of the loop parallel to line are parallel to the magnetic field, and the sides of the loop parallel to line are perpendicular to the magnetic field. The current in the loop is 350 mA, and the magnetic field strength is 0.12 T. The length of and the length of .

Find the torque acting on the loop to the nearest micronewton-meter.

Find the magnetic dipole moment of the loop to the nearest micronewton-meter per tesla.

**Q10: **

If the torque acting on a current-carrying coil whose plane makes a angle with a uniform magnetic field is 4 N⋅m, then the maximum value of torque that can act on the coil is .

- A2 N⋅m
- B3.5 N⋅m
- C8 N⋅m
- D4.6 N⋅m