Worksheet: Magnetic Force on a Straight Current-Carrying Conductor in a Magnetic Field

In this worksheet, we will practice finding the force on a straight wire in a uniform magnetic field and finding the field direction using the first right-hand rule.

Q1:

A 50.0 cm length of wire is in a 1.20 T magnetic field. The current in the wire is 8.00 A and a force of 2.40 N acts on the wire.

What is the angle between the wire and the magnetic field?

If the wire is rotated to be at an angle of 90.0 to the magnetic field, what force is exerted on it?

Q2:

A current carrying conductor is placed within regions containing magnetic fields, perpendicular to those fields. The current carrying conductor is subject to magnetic forces, as shown in the cases (a), (b), and (c). In each case, the current carrying conductor is aligned perpendicular to the magnetic field.

In what direction is the current carrying conductor aligned in case (a)?

  • Ain
  • Bright
  • Cout
  • Dleft
  • Eup

In what direction is the current carrying conductor aligned in case (b)?

  • Ain
  • Bout
  • Cdown
  • Dright
  • Eleft

In what direction is the current carrying conductor aligned in case (c)?

  • Adown
  • Bleft
  • Cup
  • Dright
  • Ein

Q3:

A current-carrying conductor is placed within regions containing magnetic fields, as shown in the cases (a), (b), (c), (d), (e), and (f).

What is the direction of the magnetic force on the current in case (a)?

  • Ain
  • Bleft
  • Cup
  • Dright
  • Eno force

What is the direction of the magnetic force on the current in case (b)?

  • Aup
  • Bdown
  • Cout
  • Dno force
  • Ein

What is the direction of the magnetic force on the current in case (c)?

  • Ain
  • Bno force
  • Cup
  • Ddown
  • Eleft

What is the direction of the magnetic force on the current in case (d)?

  • Adown
  • Bup
  • Cno force
  • Dout
  • Ein

What is the direction of the magnetic force on the current in case (e)?

  • Aright
  • Bleft
  • Cno force
  • Dup
  • Eout

What is the direction of the magnetic force on the current in case (f)?

  • Aup
  • Bno force
  • Cright
  • Ddown
  • Eout

Q4:

A 5.0 m section of a long, straight wire carries a current of 10 A while in a uniform magnetic field of magnitude 8.0×10 T.

Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is 45.

Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is 90.

Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is 0.

Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is 180.

Q5:

A long rigid wire lies along the 𝑥-axis and carries a current of 2.5 A in the positive 𝑥-direction. Around the wire is the magnetic field Bij=2.0+5.0𝑥, with 𝑥 in meters and 𝐵 in millitesla. Calculate the magnetic force on the segment of wire between 𝑥=2.0m and 𝑥=4.0m.

Q6:

A 12 A current flows along the wire shown in the diagram. The highlighted section of the wire is 0.50 cm long.

What is the magnitude of the magnetic field due to the highlighted segment of wire as measured at Point 𝐴?

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

What is the magnitude of the magnetic field due to the highlighted segment of wire as measured at Point 𝐵?

  • A 4 5 × 1 0 T
  • B 2 . 4 × 1 0 T
  • C 2 0 × 1 0 T
  • D 1 . 3 × 1 0 T
  • E 6 2 × 1 0 T

Q7:

A wire carries a 37.2 A current. A 4.74 cm long segment of the wire passes between the poles of a strong magnet with the segment aligned perpendicularly to the magnetic field of the magnet. A force of magnitude 5.23 N is exerted on the segment. Find the average strength of the magnetic field.

Q8:

A section of cable that has a length of 0.680 m carries current to a car starter motor. The cable is aligned to make an angle of 75 with Earth’s magnetic field, which has a magnitude of 5.50×10 T in the region of the cable. The magnetic field exerts a force of magnitude 6.50×10 N on the cable.

What is the current in the cable?

The cable is run between the poles of a strong horseshoe magnet, subjecting a segment of the cable of length 5.00 cm to a magnetic field of magnitude 1.92 T. What magnitude of force is exerted on this segment of cable?

Q9:

A wire aligned with the 𝑥-axis carries a current of 2.5 A that is directed in the positive 𝑥-direction. A segment of the wire that is 1.4 m long is in a region containing the magnetic field 𝐵=(1.0+2.0)×10ik T. Find the magnetic force on the segment.

  • A 0 . 1 3 k N
  • B 0 . 0 1 5 k N
  • C 0 . 0 0 9 2 j N
  • D 0 . 4 0 i N
  • E 0 . 0 0 7 0 j N

Q10:

An electromagnet produces a magnetic field of magnitude 2.1 T throughout a cylindrical region of radius 6.0 cm. A straight wire carrying a current of 33 A passes through the field, as shown in the figure. What is the magnitude of the magnetic force on the wire?

Q11:

An inventor wants to generate an emf of 110 V in a wire of length 3.00 m by moving the wire perpendicularly to Earth’s magnetic field which has a magnitude of 5.00×10 T in the region of the wire. At what speed must the wire move?

  • A 7 . 3 3 × 1 0 m/s
  • B 7 . 6 4 × 1 0 m/s
  • C 6 . 9 5 × 1 0 m/s
  • D 7 . 2 1 × 1 0 m/s
  • E 7 . 4 2 × 1 0 m/s

Q12:

A copper rod of length 3.0 m is hung from a ceiling using two springs of spring constant 258 N/m. There is a uniform magnetic field 𝐵 of magnitude 1.2 T aligned perpendicular to both the rod and the springs in a region of space that extends 0.5 m either side of the center of the rod’s length. The ends of the rod are connected by flexible copper wire across the terminals of a battery. Determine the magnitude of the change in the length of the springs when a current of 5.6 A runs through the copper rod. Assume any forces on the wire are negligible.

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