# Worksheet: Magnetic Force on a Current-Carrying Conducting Loop in a Magnetic Field

In this worksheet, we will practice calculating the magnitude of the magnetic dipole force that acts on a current-carrying loop in a uniform magnetic field.

**Q5: **

The current through a circular wire loop of radius 10.0 cm is 5.0 A. The wire loop is in a magnetic field with a magnitude of 0.20 T that is directed at a angle to the loop’s magnetic dipole moment.

Calculate the magnetic dipole moment of the loop.

What is the torque on the loop?

What is the potential energy of the dipole?

**Q6: **

The magnetic dipole moment of the iron atom is about
A⋅m^{2}.

Calculate the maximum magnetic dipole moment of a domain consisting of iron atoms.

- A A⋅m
^{2} - B A⋅m
^{2} - C A⋅m
^{2} - D A⋅m
^{2} - E A⋅m
^{2}

What would be the current in a single circular loop of wire with diameter 1.0 cm that produced the same dipole moment as that produced by iron atoms?

**Q11: **

A square loop of wire has a side length of 16.3 cm and consists of 180 turns of wire. The loop is placed in a uniform magnetic field of magnitude 1.40 T, perpendicular to the field’s direction. The wire is supplied with a current of 50.0 A.

What is the magnitude of the maximum torque on the loop?

The current is switched off, and the loop is held at an angle of from the direction of the magnetic field when the current is supplied. What is the magnitude of the maximum torque on the loop when the current is supplied again?

**Q13: **

A current loop is placed in a constant uniform magnetic field at some value of a variable angle relative to the direction of the magnetic field. For each value of , the loop is supplied with a current , where is constant for all angles of the loop.

At what value of is the torque induced on the loop of the maximum possible torque that can be produced by the loop in the field?

At what value of is the torque induced on the loop of the maximum possible torque that can be produced by the loop in the field?

At what value of is the torque induced on the loop of the maximum possible torque that can be produced by the loop in the field?

**Q14: **

A circular current loop has a radius of 76.0 cm and consists of 240 turns of wire. The loop is aligned vertically while at rest at a point on the Earth’s surface, with the loop’s axis aligned east to west. A current of 133 A is supplied to the loop clockwise as viewed from the east. The magnetic field of Earth in the region of the loop is directed north, parallel to Earth’s surface and has a magnitude of T. What is the magnitude of the torque on the loop?

**Q16: **

A circular coil with 240 turns has a radius of 2.70 cm and is in a region containing a uniform magnetic field of magnitude T. The angle between the coil’s magnetic dipole moment and the magnetic field is .

What current in the coil results in a magnetic dipole moment of 3.40 A⋅m^{2}?

What is the maximum possible magnitude of torque that the field can exert on the coil?

What is the magnitude of the torque on the coil?

What is the magnetic potential energy of the coil?

**Q17: **

A circular loop of wire of area
17 cm^{2} carries a current of
35 A. At a particular
instant , the loop lies in the -plane and is
subjected to a magnetic field T. As viewed from above the
-plane, the current is circulating clockwise.

What is the magnetic dipole moment of the current loop?

- A A⋅m
^{2} - B A⋅m
^{2} - C A⋅m
^{2} - D A⋅m
^{2}

What is the magnetic torque on the loop at the instant ?

- A N⋅m
- B N⋅m
- C N⋅m
- D N⋅m
- E N⋅m

**Q18: **

A wire of length 1.7 m is wound into a single-turn planar loop. The loop carries a current of 9.4 A and is placed in a uniform magnetic field of magnitude 0.46 T.

What is the maximum torque that the field can exert on the loop if the loop is deformed into a square?

What is the maximum torque that the field can exert on the loop if the loop is deformed into a circle?

At what angle relative to the magnetic field would the loop deformed into a circle have to be oriented for the torque on it from the field to be equal to the maximum possible torque that the field could exert on the loop when it was deformed into a square?

**Q19: **

A wire is made into a circular shape of radius 50 cm that is pivoted along a vertical central support. The two ends of the wire are in contact with a brush that is connected to a direct current generator, and a current of 145 A is supplied to the wire. The wire is placed between the poles of a magnet where a uniform magnetic field is present. In a coordinate system with origin at the center of the ring, the magnetic field is T, . The ring rotates about the -axis. Find the magnitude of the maximum torque on the ring.