Worksheet: Motion of Straight Conductors in Uniform Magnetic Fields

In this worksheet, we will practice relating the potential difference induced across straight conductors to their motion in uniform magnetic fields.

Q1:

A 15 cm long conducting rod has a potential difference across it, as shown in the diagram. The rod moves through a uniform magnetic field at 0.32 m/s. The magnitude of the induced potential difference is 9.6 mV.

What is the strength of the magnetic field?

  • A0.15 T
  • B0.050 T
  • C0.31 T
  • D0.10 T
  • E0.20 T

Which side of the field-containing region is the rod moving toward?

  • ABottom
  • BTop
  • CLeft side
  • DRight side

Q2:

A small aircraft flies at 150 m/s through a region where the strength of Earth’s magnetic field perpendicular to its wings is 35 µT. The wingspan of the aircraft is 12 m. What potential difference is induced across the aircraft’s wingtips?

Q3:

The circuit shown in the diagram contains a 4.5 V battery attached to smooth conducting rails. The ends of the conducting rails are attached to a 15 cm long conducting rod with a resistance of 2.5 Ω and a mass of 750 g. The circuit is within a 125 mT uniform magnetic field.

What is the magnitude of the acceleration of the rod?

What is the initial rate at which the potential difference across the rod decreases due to the emf induced across it because of its motion in the magnetic field?

  • A62×10 V/s
  • B1.4×10 V/s
  • C4.2×10 V/s
  • D23×10 V/s
  • E8.4×10 V/s

Q4:

The ends of a conducting rod are connected to a loop of conducting wire, as shown in the diagram. The rod enters a region that contains two oppositely directed uniform magnetic fields of equal magnitudes, where exactly half of the length of the rod is in each of the fields. The rod moves perpendicularly to both of the fields. The conducting wire does not enter either of the fields. The rod is 2 cm long and moves at 1 cm/s, and the magnetic fields are both 20 mT in strength. The total resistance of the rod and the wire is 0.5 Ω.

What is the potential difference between the ends of the rod as it moves through the fields?

What is the current through the wire as the rod moves through the fields?

What is the magnitude of the potential difference between either end of the rod and the center of the rod as the rod moves through the fields?

  • A6.2×10 V
  • B1.2×10 V
  • C2.0×10 V
  • D1.5×10 V
  • E50×10 V

Q5:

A conducting rod moves on conducting rails that form a circuit that contains two resistors, as shown in the diagram. The power dissipated by the circuit is 65.5 mW. The strength of the magnetic field the circuit is within is 945 mT. The rod has a resistance per unit length of 15 Ω/m. Find the speed 𝑣 at which the rod must move.

Q6:

A conducting rod moves on conducting rails that form a circuit that contains a resistor, as shown in the diagram. The rod travels the full distance across the rails in a time of 36 s, moving at a constant speed. The magnetic field around the circuit has a strength of 275 mT. The current in the circuit is 32 μA. Find the resistance of the rod.

Q7:

A 3.3 cm conducting rod moves through a 55 mT uniform magnetic field, as shown in the diagram. The rod travels at 8.5 cm/s, and the potential difference across the rod is 110 µV. Find the angle 𝜃.

Q8:

A 7.2 cm long conducting rod moves through a 36 mT uniform magnetic field, as shown in the diagram. The rod travels at 4.5 cm/s.

What is the magnitude of the potential difference across the rod?

  • A3.2×10 V
  • B1.2×10 V
  • C2.4×10 V
  • D0.60×10 V
  • E0.12×10 V

Which end of the rod has a higher potential?

  • AB
  • BA

Q9:

A conducting rod is rotated with one end of it held stationary. The rod rotates uniformly within a uniform magnetic field, with the direction of the rotation of the rod relative to the magnetic field varied, as shown in the diagrams I, II, III, and IV. The rod rotates at the same rate in each diagram.

In which of the diagrams does the value for the magnitude of the potential difference induced between the fixed end of the rod and the free end of the rod vary as the rod rotates?

  • AIII
  • BI
  • CII
  • DIV
  • ENone of the diagrams

Is the magnitude of the potential difference induced between the fixed end of the rod and the free end of the rod in diagram I equal to the magnitude of the potential difference induced between the fixed end of the rod and the free end of the rod in diagram II?

  • AYes
  • BNo

Is the magnitude of the potential difference induced between the fixed end of the rod and the free end of the rod in diagram III equal to the magnitude of the potential difference induced between the fixed end of the rod and the free end of the rod in diagram IV?

  • AYes
  • BNo

Is the magnitude of the potential difference induced between the fixed end of the rod and the free end of the rod in diagram I equal to the magnitude of the potential difference induced between the fixed end of the rod and the free end of the rod in diagram III?

  • AYes
  • BNo

Q10:

A conducting rod that is within a uniform magnetic field moves at a constant speed along a circular path, where the direction of the circular motion is perpendicular to the length of the rod throughout the motion. When the rod is at the positions A and C shown in the diagram, the direction of the circular motion is along the line of the direction of the magnetic field. When the rod is at the positions B and D shown in the diagram, the direction of the circular motion is perpendicular to the line of the direction of the magnetic field. The graph shows lines of four different colors. Each line could represent the change in the potential difference across the length of the rod as it moves from A to B to C to D and back to A. Which color correctly represents how the potential difference varies with time?

  • AOrange
  • BBlue
  • CRed
  • DGreen
  • ENone of these lines

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