# Introduction

A datable measure of affluence in society the average American family owns 1.88 cars but when you look at the number of induction motors in a typical home you will find dozens of them. Appliances, fans, toothbrushes, induction cooktops, wireless chargers and with improved batteries and some improved cars as such as tesla. All these devices run with respect of faradays law and rely on loop conducting wire in changing magnetic flux..

The emf more familiarly known as a voltage is the number of turns of wire and the final factor is the derivative of the flux,  it’s the rate of change. Example if the magnetic field is constant over the area loops and is perpendicular to the area then we get and we use change over an interval rather the derivative we get.

How can the field be constant over the area, and the changing over the interval we will use a stationary magnet that generates a fairly constant field and we will use the motion of the coil through that field to change the flux. The setup is as show below.

# Procedure one, phet simulation

• Opened the PHET faraday simulation software.
• Moved the magnet through the coil keeping the speed constant and noting how the bulb reacts to the motion.
• Repeated the above procedure at a faster rate but still at constant speed and commented on the differences
• Repeated the above with the coil with a different loop count and commented on the differences.

Negative sign in faraday law comes from Lenz law. In the case of the simulation the induced Emf will generate a current that will generate a magnetic field that opposes a magnetic field that opposes the field that produced it.

• Noted the polarity of the meter, which current direction lead to appositive reading.
• Dragged the magnetic field through the coil with the note pole leading and noted the meter response as it enters and as it exits.
• Reversed the magnetic field and repeated the process and noted the difference
• Related the observation to Lenz law.

# Procedure two, area of the coils

Before analyzing the data, did some preparatory steps. The emf is proportional to the area of the coils, to calculate this manufactures specification given is;

• Number of turns is 200
• Inside diameter is 1.9 cm
• Outside diameter is 3.1

Calculated the average diameter which is used to calculate the area of a loop and multiple to get an estimate of the total area of the coil

# Procedure three, measuring the field

-Used magnetic field probe, to measure the magnetic field outside, at the center and at the edge of the magnetic field.

 Run names Pole distance in cm B at the center (T) B at the edge   (T) Distance for  0 T (cm) High field 1.5 0.086 0.080 3 Low field 3.0 0.056 0.050 6

# EXPERIMENTAL ANALYSIS

## Procedure one results data analysis

Where is the magnet when the sensor bulb and meter react most strongly?

It was at the position shown below.

What happens when center of magnet passes through the coil?

There was no reaction both from bulb and the meter. The bulb did not lit bulb nor the meter deflected.

What happens as magnets exits the coil?

The bulb lighted and the meter deflected.

What happens when speed of magnet changes as it move and out of the coil?

The bulb lighted more intensely and the meter deflected more strongly. There was no relative position observable where the bulb ceased to light up.

What happens when you increase the loop count?

The current increased hence the bulb lighted up more intensely due to  flux increase.

Lenz law relation demonstration explained.

Lenz law states that, direction of electric current which is induced in a conductor by changing magnetic field is such that the magnetic field created by induced current opposes the initial changing magnetic field. Its qualitative law that explains the direction of induced current but do not states its magnitude.

As the magnet goes into the coil with North Pole leading the meter deflected to the negative voltage as its exits that’s the South Pole coming last the meter deflected to the positive voltage. As it reverses, the South Pole leading the meter deflected to the negative voltage and as it exits it deflected to the positive voltage side.

## Procedure two, calculate area of coils.

Average diameter from manufacturer specification is (1.9+3.1)/2= 2.5

A=pie*r^2=4.91

Emf= 4.91*200*0.03/3=9.82

 Run Name Pole Distance (cm) B at center (T) B at edge (T) Distance for 0 T (cm) High Field 1.5 0.086 0.080 3 Low Field 3.0 0.056 0.050 6

# Procedure four

Where is the peak of the field and what’s the emf at that time?

9.0 From the graph

Where does emf peak in relation to the field?

At the middle of the magnet

What can you say from Lenz law in relation to this graph?

A graph of coil emf against time increases then decreases to a level.

Maximum emf is obtained when the north pole fall through the coil, this is when the rate of cutting lines of force is highest because the magnet is falling faster.

As a result of velocity rate being greater the emf is shorter

So the emf is reversed because the field direction is being reversed when the poles drop through the coil because the induced current direction is also reversed.

# conclusion

Faradays law states that when a magnetic flux linking a circuit changes an electromotive force is induced in the circuit which is proportional to the rate of change of the flux linkage. PHET simulation in this experiment clearly depicts this effect with the bulb lighting before the all magnet is passed through the coils because of increased magnetic flux at that point.