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.

Q1:

A 4.0-cm by 6.0-cm rectangular current loop carries a current of 10 A. What is the magnetic dipole moment of the loop?

Q2:

A circular coil of radius 7.5 cm is wound with five turns and carries a current of 4.2 A. If the coil is placed in a uniform magnetic field of magnitude 4.5 T, what is the magnitude of the maximum possible torque that the magnetic field can exert on it?

Q3:

A conducting loop has 50 square turns with sides 15 cm long. The loop is placed in a uniform 0.80-T magnetic field. Find the current through the loop needed to create a maximum torque of 9.0 N⋅m.

Q4:

A circular coil of wire of radius 5.0 cm has 20 turns and carries a current of 2.0 A. The coil lies in a magnetic field of magnitude 0.50 T that is directed parallel to the plane of the coil.

What is the magnetic dipole moment of the coil?

What is the torque on the coil?

Q5:

The current through a circular wire loop of radius 10.0 cm is 5.0 A. The wire loop is in a 0.20-T magnetic field that is directed at a 30 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 2.1×10 A⋅m2.

Calculate the maximum magnetic dipole moment of a domain consisting of 10 iron atoms.

  • A 2 . 6 × 1 0 A⋅m2
  • B 2 . 1 × 1 0 A⋅m2
  • C 1 . 8 × 1 0 A⋅m2
  • D 1 . 5 × 1 0 A⋅m2
  • E 3 . 0 × 1 0 A⋅m2

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 10 iron atoms?

Q7:

A proton has a magnetic field due to its spin. The field is equivalent to that created by a circular current loop 0.650×10 m in radius that carries a current of 1.05×10 A. Find the magnitude of the maximum torque on a proton that can be produced by a 2.50-T magnetic field.

  • A 3 . 2 × 1 0 N⋅m
  • B 3 . 0 × 1 0 N⋅m
  • C 3 . 9 × 1 0 N⋅m
  • D 4 . 5 × 1 0 N⋅m
  • E 3 . 5 × 1 0 N⋅m

Q8:

A dc power line for a light-rail system carries a current of 1,000 A at an angle of 30 relative to Earth’s 5.0×10 T magnetic field. What is the magnitude of the force that acts on a 100-m section of this line?

Q9:

The permanent magnets in an electric motor lose 5.0% of their strength.

By how many percent is the torque of the motor decreased?

  • A 2 . 5 %
  • B 1 0 %
  • C 2 5 %
  • D 2 . 2 %
  • E 5 . 0 %

How many percent would the current to the motor need to be increased to compensate for the loss of torque by the motor?

  • A 4 . 7 %
  • B 5 . 5 %
  • C 5 . 7 %
  • D 5 . 0 %
  • E 5 . 3 %

Q10:

What is the magnetic field at 𝑃 due to the current 𝐼=0.50 A in the wire shown, where 𝑎=50 cm and 𝑏=80 cm?

  • A 5 . 2 × 1 0 T
  • B 9 8 × 1 0 T
  • C 6 . 3 × 1 0 T
  • D 3 . 2 × 1 0 T
  • E 1 . 2 × 1 0 T

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 11.6 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?

Q12:

A square loop of wire has a side length of 24.3 cm and consists of 210 turns of wire. The loop is placed in a uniform magnetic field. When a 45.5 A current is supplied to the loop, a maximum torque of magnitude 300 N⋅m is exerted on the loop. What is the magnitude of the magnetic field?

Q13:

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

At what value of 𝜃 is the torque induced on the loop 95.0% of the maximum possible torque that can be produced by the loop in the field?

At what value of 𝜃 is the torque induced on the loop 73.0% of the maximum possible torque that can be produced by the loop in the field?

At what value of 𝜃 is the torque induced on the loop 16.0% 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 3.0×10 T. What is the magnitude of the torque on the loop?

Q15:

A current-carrying coil in a magnetic field experiences a torque that is 67% of the maximum possible torque that the field can exert on the coil. What is the angle between the magnetic field and the line normal to the coil’s axis?

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 7.20×10 T. The angle between the coil’s magnetic dipole moment and the magnetic field is 60.

What current in the coil results in a magnetic dipole moment of 3.40 A⋅m2?

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 cm2 carries a current of 35 A. At a particular instant 𝑡, the loop lies in the 𝑥𝑦-plane and is subjected to a magnetic field Bijk=(6.0+3.0+2.0)×10 T. As viewed from above the 𝑥𝑦-plane, the current is circulating clockwise.

What is the magnetic dipole moment of the current loop?

  • A 0 . 0 1 5 i A⋅m2
  • B 0 . 0 1 2 j A⋅m2
  • C 0 . 0 6 0 k A⋅m2
  • D 0 . 0 1 2 j A⋅m2

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

  • A ( 0 . 1 8 + 0 . 3 6 ) i j N⋅m
  • B ( 0 . 1 8 0 . 3 6 ) i j N⋅m
  • C ( 0 . 1 8 0 . 3 6 ) i j N⋅m
  • D ( 0 . 1 8 0 . 3 6 ) j k N⋅m
  • E ( 0 . 1 8 0 . 3 6 ) i k 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 𝐵=3.2×10 T, 𝐵=𝐵=0. The ring rotates about the 𝑧-axis. Find the magnitude of the maximum torque on the ring.

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