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?

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

  • ARight side
  • BLeft side
  • CBottom
  • DTop

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?

  • A 2 3 × 1 0 V/s
  • B 6 2 × 1 0 V/s
  • C 8 . 4 × 1 0 V/s
  • D 1 . 4 × 1 0 V/s
  • E 4 . 2 × 1 0 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?

  • A 6 . 2 × 1 0 V
  • B 1 . 2 × 1 0 V
  • C 1 . 5 × 1 0 V
  • D 5 0 × 1 0 V
  • E 2 . 0 × 1 0 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.

  • A 8.4 m/s
  • B 12 m/s
  • C 67 m/s
  • D 4.2 m/s
  • E 9.5 m/s

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 .

  • A 3 0
  • B 1 2 0
  • C 6 5
  • D 4 5
  • E 9 0

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