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Worksheet 10: Electromagnetic Induction in a Solenoid

Introduction

In this lab, you will investigate Faraday’s Law of Electromagnetic Induction and Lenz’s Law by observing and measuring the effects of a falling magnet through a solenoid. As the magnetic flux through the coil changes due to the motion of the magnet, an electromotive force (EMF) is induced, generating a current in the circuit. This experiment demonstrates how magnetic fields interact with conductors and explores energy conversion between kinetic and electric energy.

Faraday’s and Lenz’s Laws

Faraday’s Law states that a change in magnetic flux through a circuit induces an EMF:

\mathcal{E} = -\frac{d\Phi_B}{dt}

Where: - \mathcal{E} is the induced EMF, - \Phi_B is the magnetic flux.

Lenz’s Law explains the direction of the induced current: it opposes the change in magnetic flux that produced it. This opposition can be observed both qualitatively (e.g., LEDs flashing and magnet slowing in a copper collar) and quantitatively (e.g., through voltage and power measurements).

As the magnet falls through the solenoid, it induces a voltage that briefly lights an LED or causes a current to flow through a resistor. This experiment also explores energy conservation, comparing the magnet’s kinetic energy loss with the electrical energy generated in the circuit.

Overview of Measurements

Measurement 1: Qualitative Observations of Electromagnetic Induction

  • A cylindrical magnet is dropped through a transparent tube inside a solenoid.
  • The solenoid is connected to LEDs, and you observe the flashing pattern as the magnet passes through.
  • The direction of the induced current is inferred based on which LED lights up and when.
  • Using an oscilloscope, the induced voltage is captured and analyzed for waveform shape.
  • A copper collar is placed over the tube to observe how eddy currents slow the magnet, providing a visual example of Lenz’s Law.

Measurement 2: Quantitative Study of Induction and Energy Conversion

  • The LEDs are replaced by a 5-ohm resistor, and the induced voltage is measured with an oscilloscope.
  • A photogate sensor records the magnet’s velocity as it exits the tube.
  • These measurements are repeated with and without the resistor to determine how the circuit affects the magnet’s motion.
  • Using Ohm’s Law and power formulas, the induced current and power vs. time are calculated.
  • Energy analysis:
  • Electrical energy: computed by integrating power over time.
  • Kinetic energy: calculated from the velocity data.
  • The energy loss due to induction is compared to the electrical energy generated, offering insight into efficiency and conservation of energy in electromagnetic systems.

Objectives

By the end of this lab, you will be able to: - Apply Faraday’s Law and Lenz’s Law to explain real-world electromagnetic phenomena. - Observe and interpret induced currents using LEDs and oscilloscopes. - Measure the velocity of a falling magnet and calculate its kinetic energy. - Use oscilloscope data to calculate induced voltage, current, power, and electrical energy. - Compare kinetic energy loss to electrical energy output, discussing the efficiency of energy conversion. - Understand how eddy currents and resistive loads influence motion and induction.

Materials List

  • Solenoid and Transparent Plastic Tube
  • Cylindrical Magnet (marked with North Pole indicator)
  • LEDs
  • Copper Collar
  • Oscilloscope
  • Digital Multimeter (DMM)
  • 5 Ω Resistor
  • Dual-Beam Photogate
  • Capstone Software
  • USB Drive
  • Scale (for measuring magnet mass)