Worksheet: Electromagnetic Interactions in Conducting Loops 

In this worksheet, we will practice analyzing the current induced in conducting loops by changing magnetic fields and the magnetic field due to a current loop.

Q1:

A circular conducting loop has a radius 𝑟 . The north pole of a permanent magnet faces perpendicularly to the plane of the loop, as shown in the diagram. The permanent magnet is moved in the positive 𝑧 -direction. Also shown in the figure are the magnetic field lines from the north pole that intersect the loop at points 𝐴 and 𝐵 .

Which of the following is the direction of the current induced in the loop at point 𝐴 within the plane of the loop?

  • AThe positive 𝑥 -direction
  • BThe positive 𝑦 -direction
  • CThe negative 𝑥 -direction
  • DThe negative 𝑦 -direction

Which of the following is the direction of the current induced in the loop at point 𝐵 within the plane of the loop?

  • AThe negative 𝑦 -direction
  • BThe positive 𝑥 -direction
  • CThe positive 𝑦 -direction
  • DThe negative 𝑥 -direction

Which of the following is the direction of the magnetic field that is produced by the current induced in the loop?

  • ACounterclockwise around the loop
  • BClockwise around the loop
  • CThe positive 𝑧 -direction
  • DThe negative 𝑧 -direction

Q2:

A conducting coil with a radius of 4.5 cm has 120 turns. The coil moves perpendicularly to a magnetic field that decreases in strength from 15 mT to 11 mT. A 12.5 mV emf is induced while the coil moves. Find the time for which the coil moves.

Q3:

A conducting coil with a radius of 2.5 cm has 150 turns. The coil moves perpendicularly to a magnetic field that becomes stronger at the rate of 1.8 mT/s. Find the magnitude of the electromotive force induced in the coil.

  • A 0.53 mV
  • B 0.021 mV
  • C 4.6 mV
  • D 350 mV
  • E 11 mV

Q4:

A conducting coil has an area of 8 . 6 8 × 1 0   m2. The coil moves perpendicularly to a magnetic field that increases in strength from 12 mT to 16 mT in 0.14 s during which an 18.6 mV electromotive force is induced in the coil. How many turns does the coil have?

Q5:

A conducting coil has a radius 𝑟 = 1 3 c m and 35 turns. The coil is moved so that half of its area is within a uniform magnetic field of strength 0.16 T, directed out of the plane of the diagram shown along the axis of the coil. The coil moves from its old position to its new position in 0.24 s.

What is the magnitude of the electromotive force induced in the coil?

Is the current through the coil clockwise or counterclockwise?

  • AClockwise
  • BCounterclockwise

Q6:

A circular loop of conducting wire with a radius 𝑟 carries a constant current in the counterclockwise direction, as shown in the diagram. The magnetic field produced due to the current at the points 𝐴 and 𝐵 is shown. The field due to the current at point 𝐴 is shown in the 𝑥 𝑧 -plane of the coordinate system and the field due to the current at point 𝐵 is shown in the 𝑦 𝑧 -plane of the coordinate system.

At which of the following points is the magnetic field due to the current greatest?

  • AAt the origin of the coordinate system
  • BAt a point 2 𝑟 in the 𝑧 -direction from the origin of the coordinate system
  • CAt a point 2 𝑟 in the 𝑥 -direction from the origin of the coordinate system
  • DAt a point 2 𝑟 in the 𝑦 -direction from the origin of the coordinate system

Which of the following is the direction of the magnetic field at the origin of the coordinate system?

  • AThe negative 𝑧 -direction
  • BThe positive 𝑧 -direction
  • CThere is no magnetic field at the origin of the coordinate system.

Which of the following is the direction of the magnetic field at a point 2 𝑟 in the negative 𝑦 -direction from the origin of the coordinate system?

  • AThe positive 𝑧 -direction
  • BDirectly toward the origin of the coordinate system
  • CDirectly away from the origin of the coordinate system
  • DThe negative 𝑧 -direction

Q7:

A loop of conducting wire has a radius of 28 cm. The loop is in a uniform magnetic field of strength 125 mT that is out of the plane of the diagram shown and parallel to the axis of the loop. The loop is rotated in 0.45 s to face in a direction that is at an angle of 6 5 ∘ from its original axial direction. What is the magnitude of the electromotive force induced in the loop?

Q8:

A conducting coil with four turns has a diameter 𝑑 = 2 5 c m . The coil moves 1.5 cm at a velocity 𝑣 = 7 . 5 / c m s parallel to the axis of a stationary bar magnet, as shown in the diagram. An emf of magnitude 3.6 mV is induced in the coil while it moves past the magnet. Find the change in the magnetic field strength between the points where the coil started to move and where it stopped moving.

  • A 8 . 9 × 1 0   T
  • B 7 . 4 × 1 0   T
  • C 9 . 2 × 1 0   T
  • D 3 . 7 × 1 0   T
  • E 1 . 8 × 1 0   T

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