Worksheet: Induced Electric Fields

In this worksheet, we will practice using Faraday's law to calculate the magnetic and electric fields produced through electromagnetic induction.

Q1:

A 50-turn coil with a diameter of 15 cm is placed in a spatially uniform magnetic field of magnitude 0.50 T. The face of the coil and the magnetic field are perpendicular to each other. Assume that the magnetic field is cylindrically symmetric with respect to the central axis of the coil. Calculate the magnitude of the electric field induced if the magnetic field is reduced to zero in 0.10 seconds.

Q2:

Over a region of radius 𝑅, there is a spatially uniform magnetic field B (shown in the figure). At 𝑡=0, ||=1.0BT, after which B decreases to 0 T in 30 seconds at a constant rate. Protons can move in the region of the magnetic field. The charge of a proton is 1.60×10 C.

If 𝑅=10.0cm, how much work is done by the induced electric field in the region on a proton that moves once around a clockwise circular path of radius 5.0 cm?

  • A 2 . 6 × 1 0 J
  • B 4 . 7 × 1 0 J
  • C 3 . 8 × 1 0 J
  • D 3 . 1 × 1 0 J
  • E 4 . 2 × 1 0 J

At an instant when B=0.50T, a proton enters the magnetic field at 𝐴, moving at 5.0×10 m/s. What is the magnitude of the magnetic force on the proton at that instant?

  • A 3 . 5 × 1 0 N
  • B 4 . 8 × 1 0 N
  • C 4 . 4 × 1 0 N
  • D 4 . 0 × 1 0 N
  • E 5 . 0 × 1 0 N

At an instant when B=0.50T, a proton enters the magnetic field at 𝐴, moving at 5.0×10 m/s. What is the magnitude of the electric force on the proton at that instant?

  • A 3 . 0 × 1 0 N
  • B 3 . 9 × 1 0 N
  • C 3 . 2 × 1 0 N
  • D 2 . 7 × 1 0 N
  • E 3 . 5 × 1 0 N

Q3:

The current in a long solenoid of radius 3.0 cm and 480 turns per meter is varied with time at a rate of 2.0 A/s. A circular loop of wire with a radius of 5.0 cm and a resistance of 2.0 Ω surrounds the solenoid. Find the current induced in the loop.

Q4:

A circular copper disk of radius 7.5 cm rotates at 2,400 rpm around the axis through its center and perpendicular to its face. The disk is in a uniform magnetic field B of strength 1.2 T that is directed along the axis. What is the potential difference between the rim and the axis of the disk?

Q5:

Shown in the following figure is a long, straight wire and a single-turn rectangular loop, both of which lie in the plane of the page. The wire is parallel to the long sides of the loop and is 0.50 m away from the closer side. At an instant when the emf induced in the loop is 2.0 V, what is the time rate of change of the current in the wire?

  • A 3.3 A/s
  • B 3.0 A/s
  • C 2.5 A/s
  • D 1.7 A/s
  • E 2.0 A/s

Q6:

Suppose the parallel plate capacitor shown is accumulating charge at a rate of 0.035 C/s. What is the magnitude of the resulting induced magnetic field at a distance of 15 cm from the capacitor?

  • A 4 . 7 × 1 0 T
  • B 5 . 1 × 1 0 T
  • C 6 . 9 × 1 0 T
  • D 3 . 2 × 1 0 T
  • E 3 . 8 × 1 0 T

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