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 negative 𝑦-direction
  • CThe negative 𝑥-direction
  • DThe positive 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 positive 𝑥-direction
  • BThe negative 𝑥-direction
  • CThe positive 𝑦-direction
  • DThe negative 𝑦-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
  • BThe positive 𝑧-direction
  • CClockwise around the loop
  • 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.

Q4:

A conducting coil has an area of 8.68×10 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=13cm 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 𝑥𝑧-plane of the coordinate system and the field due to the current at point 𝐵 is shown in the 𝑦𝑧-plane of the coordinate system.

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

  • AAt a point 2𝑟 in the 𝑥-direction from the origin of the coordinate system
  • BAt a point 2𝑟 in the 𝑧-direction from the origin of the coordinate system
  • CAt a point 2𝑟 in the 𝑦-direction from the origin of the coordinate system
  • DAt 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 positive 𝑧-direction
  • BThere is no magnetic field at the origin of the coordinate system.
  • CThe negative 𝑧-direction

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

  • AThe negative 𝑧-direction
  • BDirectly away from the origin of the coordinate system
  • CDirectly toward the origin of the coordinate system
  • DThe positive 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 65∘ 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=25cm. The coil moves 1.5 cm at a velocity 𝑣=7.5/cms 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.

  • A1.8×10 T
  • B3.7×10 T
  • C9.2×10 T
  • D7.4×10 T
  • E8.9×10 T

Q9:

A coil with 4 turns has a diameter 𝑑=16cm. A bar magnet moves 1.2 cm into the coil at an angle of 36∘ to the axis of the coil in a time of 0.16 s. An emf of 4.1 mV is induced in the coil. How much does the average magnetic field strength of the magnet decrease 1.2 cm from its poles?

Q10:

A coil with 5 turns and a 16 cm radius rotates around an axis that is perpendicular to a uniform magnetic field, as shown in the diagram. The coil completes 12 rotations per second. The electromotive force induced in the coil is 255 mV. What is the strength of the magnetic field?

Q11:

A conducting coil has a radius 𝑟=18 cm and 25 turns. The coil is moved so that half of its area is within a uniform magnetic field of strength 0.12 T, directed out of the plane of the diagram shown along the axis of the coil. An electromotive force of 0.33 V is induced while the coil moves. What is the average speed at which the coil moves?

Q12:

A coil with 6 turns and a radius of 2.1 cm is placed with the center of its base at the center of the base of a coil with four turns and a radius of 7.2 cm, as shown in the diagram. The top of the smaller coil is below the top of the larger coil. The larger coil is connected to a variable voltage source and a current is induced in the larger coil that produces a uniform magnetic field inside it, which changes from zero magnitude to a magnitude of 360 mT in a time of 23 ms.

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

Is the current through the smaller coil clockwise or counterclockwise?

  • ACounterclockwise
  • BClockwise

Q13:

A coil with 5 turns and a 12 cm radius rotates around an axis that is perpendicular to a uniform magnetic field, as shown in the diagram. The coil has a resistance of 25 Ω and completes 15 rotations per second. The strength of the magnetic field is 28 mT. What is the current induced in the coil?

Q14:

A coil with 10 turns and an area of 0.0088 m2 is equidistant between two magnets, as shown in diagrams (a) and (b). When the opposite poles of the magnets move toward the coil, as shown in diagram (a), the electromotive force induced in the coil is 2.5 mV. When the like poles of the magnets move toward the coil, as shown in diagram (b), the electromotive force induced in the coil is 1.1 mV. In both cases, the magnets move the same distance as each other and for the same time of 0.25 s.

What is the magnitude of the magnetic field change that induces the electromotive force in the coil due to the motion of the weaker magnet?

  • A0.0020 T
  • B0.0031 T
  • C0.031 T
  • D0.020 T
  • E0.0062 T

What is the magnitude of the magnetic field change that induces the electromotive force in the coil due to the motion of the stronger magnet?

  • A0.02 T
  • B0.032 T
  • C0.0051 T
  • D0.012 T
  • E0.007 T

Q15:

A loop of wire with radius 15 cm moves perpendicularly to a uniform 0.25 T magnetic field at a constant speed, as shown in the diagram. The motion takes 1.5 s to complete. Find the electromotive force induced in the loop.

  • A0.024 V
  • B0 V
  • C0.036 V
  • D0.012 V
  • E0.0059 V

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