In the early part of the 19th century electricity and magnetism were seen as two discrete areas of physics. With the experimental work of Michael Faraday, and later the mathematical analysis of James Clerk Maxwell, these two areas of physics were unified by the theory of electromagnetism.
What was discovered is that moving charges, in magnetic fields will experience a forces. In essence, this is due to the fact that moving charges generate magnetic fields which thereby interact with the magnetic fields that they are in.
This is the principle behind electric motors
What was also discovered was that electric charges experiencing changing magnetic fields, or changes of flux, would experience a force and thus an EMF generated.
This underpins the concept of electrical generation.
The following lessons examines the key physical principles and mathematical models that underpin these behaviours.
What was discovered is that moving charges, in magnetic fields will experience a forces. In essence, this is due to the fact that moving charges generate magnetic fields which thereby interact with the magnetic fields that they are in.
This is the principle behind electric motors
What was also discovered was that electric charges experiencing changing magnetic fields, or changes of flux, would experience a force and thus an EMF generated.
This underpins the concept of electrical generation.
The following lessons examines the key physical principles and mathematical models that underpin these behaviours.
0. Hand Rules Explained 
Before we continue it's an important to learn the hand rules that are used in studying electromagnetism.
Hand rules are 'tool's used to establish the correct relationship between the vectors of electrical current, force, EMF and magnetic field. There are two in predominant use the first is Fleming's hand rules the second is the Palm rule. This video discusses both. Both are equally valid, however it is best to consistently use one or the other. 

1. Charge behaviour in an Electric field
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Plasma Ball
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We know that charges experience forces in electric fields. So how do these fields affect the charge whilst it is in motion? This video, using the example of a crook tube, examines the mathematical principles behind the force on moving charges within an Electric field. There's a worked solution and problems available, as well examination of a plasma ball which works under the same principles. 
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Plasma Ball

You will find plasma balls in novelty shops, but how do they work? There is more than what meets the eye, so watch and find out.


Part 2 of my plasma ball videos  where I demonstrate a number of experiments but also explain them

Interactive
This is a simulation of a charged particle being shot into a uniform electric field. By Tom Walsh
problems
 A positive test charge of 6.5 x 10^6 C experiences a force of 4.5 x 10^5 N. What is the magnitude of the electric field intensity? (6.9 N/C)
 An electric field of intensity 150 V/m exists between two plates separated by 4.0 m. What is the potential difference between the plates? (600V)
 A potential difference of 0.90 V exists from one side to the other of a cell membrane that is 5.0 x 10^9 m thick. What is the electric field across the membrane? (1.8 x 10^8 N/C)
2. Charge behaviour in an Magnetic field
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A moving charge, by its nature, generates a magnetic field. This means if the moving charge enters an external magnetic field, it will experience a force.
The force that it experiences is always perpendicular to both the magnetic field, and the direction of motion of the charges. This video examines the physical principles as well as the mathematical models that allow you to understand what is occurring. There's a work solution and problems for you to attempt, and an interactive to help deepen your understanding. 
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 An unknown particle having a mass of 2.2 x 10^27 kg and a charge of 3.3 x 10^–19 C passes through a magnetic field of 5.4 x 10^1 T. The velocity of the particle is 6.4 x 103 m/s. What is the radius of its path? (7.9 x 10^5 m)
 A particle with a mass of 3.8 x 10^27 kg and a charge of 6.2 x 10^–19 C crosses a magnetic field that measures 2.7 x 10^2 T. The particle assumes a circular path with a radius of 1.5 x 10^1 m. At what speed is the particle moving? (660, 790 m/s)
 A particle passing through a magnetic field has a mass of 6.3 x 10^–27 kg and is moving at 3.9 x 10^4 m/s. The charge on the particle is 2.4 x 10^18 C and the radius of its circular path through the field is 4.4 x 10^2 m. What is the strength of the magnetic field? (0.00233 T)
 A particle with a mass of 3.34 x 10^27 kg and a charge of 1.2 x 10^19 C passes through a magnetic field of 3.4 x 10^3 T. This causes the nucleus to assume a circular path with a radius of 0.065 m. What is its velocity? (4940.1 m/s)
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This is a simulation of a charged particle being shot into a magnetic field. It can be used to explore relationships between mass, charge, velocity, magnetic field strength, and the resulting radius of the particle's path within the field. By Tom Walsh
3. Magnetic Field around a wire
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In the early 1800s scientists were intrigued by the fact that a wire carrying an electrical current would cause a compass needle to deflect. It is Michael Faraday who established that magnetic fields which he described as lines of force, where circular.
We now know that it is actually the charges them cells namely the electrons that emit that generate magnetic fields due to their motion This video looks at the relationship between current and the magnetic field it generates 
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4. Solenoids Explained
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So how does a straight wire with a circular magnetic field get used to make an electromagnet, or a solenoid? This video looks at the physics.

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The following activity is more related to the magnetic field around a wire, or more specifically the magnetic field between two wires.
This Desmos activity allow you to see qualitatively the strength of the field between (and on either side) two wires. The wires are the asymptotes of the graph represents the wires
By sharing the current (which can be reversed by making them negative) you effectively see if there are places that exist where the B field is zero, andwhee they are a minimum
the 'k' value represents µ/2π though( its value isn't that large) and can be left alone. Changing it does not change the trend of the graph
The derivative is shown to show that a minimum can exist ate certain points
This Desmos activity allow you to see qualitatively the strength of the field between (and on either side) two wires. The wires are the asymptotes of the graph represents the wires
By sharing the current (which can be reversed by making them negative) you effectively see if there are places that exist where the B field is zero, andwhee they are a minimum
the 'k' value represents µ/2π though( its value isn't that large) and can be left alone. Changing it does not change the trend of the graph
The derivative is shown to show that a minimum can exist ate certain points
4. Examining the motor effect
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Since a current bearing wire has a magnetic field, placing the same wire in an external magnetic field will mean it will experience a force. This is known as the motor effect. See Resources for using a current balance which examine the motor effect 
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A current balance is a tool used in school to examine the motor effect. Its basically a swing which experiences a force upward on one side due to the motor effect, and a weigh on the other which counter balances it

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5. The force between two wires
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In the previous videos we discussed that a current bearing wire will generate a magnetic field. What if we placed another card bearing wire in that magnetic field? We now have two current bearing wires that are in each other's magnetic field and due to the motor effect, both should experience forces. This video examines this key principle and the mathematical models that explain it. 
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going deeper
There are a number of ways we can explore this concepts further.
One aspect of most high school physics course on kinematics, is that they only concern themselves with constant acceleration. In reality however, acceleration, like displacement and velocity, can chance with respect to time.
Velocity is the rate of change of displacement. Unit: m/s^{2}
Acceleration is the rate of change of velocity.
So what is the rate of change of acceleration?
The answer to that is the jerk. So slope of the acceleration vs time graph is the jerk. Unit: m/s^{3}
We can go further. What is the rate of change of the jerk?
Well it's the snap. Unit: m/s^{4}
Can we go further? Yep. The rate of change of snap is the crackle. Unit: m/s^{5}
I think you can guess the next one.
We can go further. What is the rate of change of the jerk?
Well it's the snap. Unit: m/s^{4}
Can we go further? Yep. The rate of change of snap is the crackle. Unit: m/s^{5}
I think you can guess the next one.
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 pHET graphing animation  this interactive from the University of Colorado pHet team is a great way to demonstrate the relationship between motion and its graphical analysis. That why I used it in my video. At this time its Java based so will only work on PC/Mac
6. Two applications
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Here are two applications that rely on the motor effect to work 
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7. How a DC motor works
8. How well do you know charge behaviour in fields?
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Test your understanding of charges in fields. So do the Quiz and try to get full marks
Then check your understanding if necessary with the video 

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9. How well do you know the motor effect?
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Test your understanding of motor effect. So do the Quiz and try to get full marks Then check your understanding if necessary with the video 

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