Faraday's Electromagnetic Lab

Theoretical Background / Context of Faraday Electromagnetic Induction

• Electromagnetic induction was discovered independently by Michael Faraday in 1831 and Joseph Henry in 1832. Faraday firstly published the result of his experiment. 
• He explained electromagnetic induction using a concept he called line force. However, this idea was widely rejected at that time, mainly because it lacked mathematical formulation. 
• James Clerk Maxwell grabbed this opportunity and used Faraday’s idea as the basis of his quantitative electromagnetic theory.

Part I: Magnetic Flux and Faraday's law of induction

• According to Faraday's Law of Induction, a changing magnetic flux through a coil induces an emf given by:

Ɛ=-Nddt

Where = B× dA = BA for a magnetic field (B) 

• which is constant over the area (A) and perpendicular to the area. N is the number of turns of wire in the coil. 
• For the simulation of electromagnetic induction, the area of the coil is constant and as the coil passes into or out of the magnetic field, there is an average emf given by:

Ɛ=-NAdBdt

Part II: Energy conversion for an induction coil swinging in a magnetic field

• In Faraday's experiment, to investigate electromagnetic energy conversion, a resistive load is connected to the coil of an induction wand which swings in the magnetic field. 
• In a resistive load, electrical power is dissipated as heat. The power dissipated in the resistor is calculated by measuring the voltage across the load resistor. 
• The energy converted to thermal energy is determined from the power versus time graph. This energy is compared to the loss of potential energy determined from the amplitude of the pendulum.
• Let L is the distance from the axis of rotation to the center of mass. If the center of mass of the pendulum starts from rest at a height h, its potential energy is

U=mgh=mgL(1-cos )

• The height h is measured from the lowest position of the center of mass as shown in the following figure. If the initial and final heights are hi and hf respectively, then the energy lost is

∆U=mg(hi-hf)

Where hi=L-Lcosi and hf=L-Lcosf

• According to the conservation of energy, it will be equal to the energy lost to friction, and energy converted to electrical energy. 
• For a resistive load in the circuit (R), the electrical energy is then dissipated as thermal energy. Induced emf (Ɛ) in the circuit is  Ɛ=IR+Ir
• Where r is the resistance of the coil itself, and I is the current in the circuit. Since R and r in series the power (P=IƐ) in the following circuit is given by:

P=I2R+r=(VR)2(R+r)

Where V is the voltage across the external resistor, V=IR. Thermal energy dissipated in the resistor (R) is given by:

E=P dt = Area under power (P) versus t graph.

Principle Work Electromagnet Virtual Lab

•  In Faraday's electromagnetic lab simulation, a voltage is induced in a coil swinging through a magnetic field. Faraday's Law and Lenz' Law are examined and the energy dissipated in a load resistor is compared to the loss of amplitude of the coil pendulum.

• In the electromagnetic induction simulation, a rigid pendulum with coil at its end swings through a horseshoe magnet. 
• A resistive load is connected across the coil and the induced voltage is recorded using a Voltage Sensor and the angle is measured with a Rotary Motion Sensor that also acts as a pivot for the pendulum. 
• The induced voltage is plotted versus time and angle. The power dissipated in the resistor is calculated from the voltage and the energy converted to thermal energy is determined by finding the area under the power versus time curve. 
• This energy is compared to the loss of potential energy determined from the amplitude of the pendulum.
• Faraday's Law is used to estimate the magnetic field of the magnet from the maximum induced voltage. 
• Also, the direction of the induced voltage as the coil enters and leaves the magnetic field is examined and analyzed using Lenz' Law