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Imagine a current carrying wire placed between two permanent magnets. Note that above the wire both the permanent magnetic field and the field generated by the ...
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Magnets can _________________ or _______________ other magnets. They are able to exert forces on each other without touching because they are surrounded by ____________________ _________________.
Magnetic Flux refers to…
Areas with many lines have __________________ magnetic field.
Magnets have two different ends called ___________________, either as_________________ (N) or ___________________ (S).
It is important to note that magnetic fields are ____________________ and therefore we need to represent the lines as…
In fact we define the direction of a magnetic field as …
This is very much like electric charges; however there is a very important difference between these two. Electric charges can be…
Whereas magnetic poles…
We can sum up the behaviour of interacting magnetic fields:
Consider a compass:
A compass is useful because its needle always points north. This is because the needle is a ________________ and so is ______________.
Yeah fine but WHY does it point north?
Well, the north pole of the compass will…
Well that’s all very well for magnetism, but where does the electro come in?
It turns out that any….
In fact a current carrying wire will have a very regular magnetic field around it as predicted by the:
1 st^ Right Hand Rule:
Solenoids: aka _____________________ A solenoid is simply…
The many loops of wire each carry current and therefore…
The 2nd^ Right Hand Rule:
Note when using any right hand rules that…
Just as with a bar magnet a solenoid has…
Note from the diagram that the field outside of a solenoid is _____________ and ______ _______________ especially if its ________________ is much greater than its _____________.
However the magnetic field inside the solenoid is ________________ and _________________________.
In a uniform magnetic field INSIDE a solenoid we can calculate the strength of the field using:
Where : B =
=
I =
n =
Example: A hollow solenoid is 25 cm long and has 1000 loops. If the solenoid has a diameter of 4.0 cm and a current of 9.0 A what is the magnetic field in the solenoid?
With permanent magnets _______________ poles attract and ________________ poles repel.
As we have seen magnetic fields surround any…
Therefore it stands to reason that magnetic forces will act on wires carrying __________________ _____________________ and charged particles moving in ______________________ _________________.
Parallel Current Carrying Wires
Picture two parallel wires carrying current in the same direction, would the fields produced by these wires attract or repel?
Parallel wires with current flowing in the same direction will…
Current Carrying Wires in Magnetic Fields A current carrying wire in a magnetic field will also experience…
Imagine a current carrying wire placed between two permanent magnets.
Note that above the wire both the permanent magnetic field and the field generated by the wire point…
These two fields will ____________________.
Also, below the wire the permanent magnetic field and the field generated by the wire point…
These two fields will ____________________.
The same logic can be used to determine how parallel wires containing currents the flow in the opposite direction interact.
Parallel wires with current flowing in the opposite directions will…
Example: Circular particle accelerators use magnetic fields to bend beams of charged particles. This allows them reach
phenomenal speeds in relatively small spaces. The cyclotron at UBC’s TRIUMF contains the largest of its kind in the world. It accelerates a beam of hydrogen anions (H-) to 75% the speed of light and uses a 0.42 T magnetic field. Note that at these speeds the relativistic mass of a hydrogen anion is 2.524x10-27^ kg. What is the outer radius of the cyclotron?
If a charged particle enters a magnetic field traveling perpendicular to the field, it will deflect continuously and travel in a _____________________. Consider an electron moving through a magnetic field
X X X X
X X X X
X X X X
X X X X
Now consider a proton moving through the same magnetic field
X X X X
X X X X
X X X X
X X X X
When charged particles travel in a circular path:
Motors We have seen that a current carrying wire perpendicular to a magnetic field will experience a _________________.
This phenomenon is used by an electric motor to transform ______________ energy into ______________ energy.
A simple DC motor consists of a loop of wire that passes through a magnetic field. The ends of the loop are attached to a split ring (______________________) which turns with the loop. Fixed ______________________ connect the commutator to the voltage source.
The commutator (split ring) is important because…
Galvanometers A galvanometer is an instrument used to detect electric current. A galvanometer calibrated to measure current is called an ________________ while one that measures voltage is called a ___________________.
These devices also make use of the motor principle.
Essentially , a current carrying wire in a magnetic field will experience a force proportional to the ______________________.
As shown on the right, when a current flows through the wire the needle will experience a force. The needle is attached to a spring which provides a restorative force. As the coil rotates against the spring a reading is produced
A galvanometer can be converted into an ammeter by placing a shunt (wire) of low resistance parallel to the coil. In other words a parallel path for electrons so that only a small fraction of electrons flow through the coil.
A galvanometer can be converted into a voltmeter by placing a shunt (wire) of high resistance in series with the coil. This greatly reduces the current that flows through the meter.
In this case where the electrons are undeflected, we know that the electrostatic and magnetic forces are
Or simply, ______________. This can be used to solve for the velocity of the electrons, which in turn allowed Thompson to determine the charge to mass ratio of the electron long before either quantities were understood.
Mass Spectrometers
Mass spectrometers can be used to determine the mass of unknown substance or to separate similar compounds of slightly different mass. First the sample is vaporized and then it is bombarded with electrons. These high energy electrons ionize the sample by knocking loose electrons. These cations are then accelerated by a potential difference and then fired into a perpendicular magnetic field. This field causes them to bend until they strike a detector.
How can this be used to determine the mass of an unknown sample?
In practice even a pure substance will strike the detector at multiple locations. Explain why this might occur.
Mass spectrometers can also be used to separate substances into individual isotopes. For example uranium naturally exists as a mixture of Uranium-238 and Uranium-235. Describe how this is done. On the diagram above, which paths (m 1 or m 2 ) would represent U-235 and U-238?
Example: Charged particles traveling horizontally at 3.60x10^6 m/s when they enter a vertical magnetic field of 0.710 T. If the radius of their arc is 9.50x10-2^ m, what is the charge to mass ratio of the particles?
Example: What is the speed of an electron that passes through an electric field of 6.30x10^3 N/C and a magnetic field of 7.11x10-3^ T undeflected? Assume the electric and magnetic fields are perpendicular to each other.
After scientists had discovered that an electric current can generate a magnetic field the logical question followed: “If an electric current can generate a magnetic field, can a magnetic field generate an electric current?” Michael Faraday and Joseph Henry independently discovered they could.
Electromagnetic Induction:
Faraday discovered many ways to induce a current. For example in the induction coil shown below.
What was most interesting to note was that…
This showed that magnetic fields do not simply create electric currents, rather they are only generated by…
Another example of this comes when you move a bar magnet into or out of a hollow solenoid.
When the magnet is moved one way the current is in one direction and when it is moved the other way the current reverses.
To predict the direction of the induced current we use Lenz’s Law :
Lenz’s Law is really an application of…
Remember that we can use the 2 nd^ Right Hand Rule to relate the poles of an electromagnet and the direction of current flow.
Thumb: Fingers:
Note that magnetic flux is at a maximum when the loop is…
And at a minimum when the loop is…
As we said the electric current is generated by a…
In order to calculate the EMF generated we need to use the idea of magnetic flux.
Magnetic Flux:
For a loop of wire in a magnetic field the magnetic flux depends on:
(1)
(2)
(3)
Example:A 0.75 m conducting rod is moved at 8.0 m s across a 0.25 T magnetic field along metal rails. The electrical resistance of the system is 5.0 Ω. What are the magnitude and direction of the current through point X?
We have already seen that a loop rotating in a magnetic field will generate an EMF according to Faraday’s Law ( )
However when considering a conductor moving in a magnetic field it is better to consider a different form of this equation.
For Moving Conductors: Where: ε = B = l = v =
Derivation :
Example: A conducting rod 25.0 cm long moves perpendicular to a magnetic field (B = 0.20 T) at a speed of 1.0 m/s. Calculate the induced EMF in the rod.
Example: A conducting rod 15 cm long moves at a speed of 2.0 m/s perpendicular to a 0.30 T magnetic field. If the resistance of the circuit is 4.0 ohms, what is the magnitude of the current through the circuit?
Devices that use mechanical energy to induce an electric current are called ________________________. Many kinds of mechanical energy can therefore by converted into electrical energy such as in: ___________________________ and ___________________________.
Note that this works in the exact opposite manner as an electric motor. Motor: _____________________ energy to _________________ energy Generator: __________________ energy to _________________ energy
Notice that these generators produce __________________ current because…
Remember that to determine the direction of the current through a loop we can use ___________________ _______________ _____________ and to determine the EMF produced by a loop we can use _____________________________ _____________ ( ).
This brings up an inherent problem with all electric motors. As we said, electric motors are basically _________________ of ______________ rotating in a _____________________ ______________.
However, we know that whenever we rotated wires in a magnetic field we generate an ___________________ __________________.
We also know from Lenz’s Law that the induced EMF works in the ________________ ___________________.
This is called:
And it always works…
Example: A 120 V motor draws 12 A when operating at full speed. The armature has a resistance of 6.0 ohms. a) Find the current when the motor is initially turned on.
b) Find the back EMF when the motor reaches full speed.
Back EMF can be calculated using:
Where: Vback =
ε =
I =
r =
Example: The diagram shows a 0.010 kg metal rod resting on two long horizontal frictionless rails which remain 0.40 m
apart. The circuit has a resistance of 3.0 Ω and is located in a uniform 0.20 T magnetic field.
a) What is the initial acceleration of the bar?
b) What is its top speed?
Example: The diagram below shows a pair of horizontal parallel rails 0.12 m apart with a uniform magnetic field of 0.055 T directed vertically downward between the rails. There is a glider of mass 9.5x10-2^ kg across the rails. The internal resistance of the 75 V power supply is 0.30 ohms and the electrical resistance of the rails and the glider is negligible. Assume friction is also negligible.
a) What is the initial acceleration of the glider?
b) What is the value of the terminal velocity as limited by the back emf produced by the moving glider?
To determine the voltage change we use the following:
Where: Vp =
Vs =
Np =
Ns =
Although we may change the voltage, we must conserve _____________.
Therefore, _________________ must also be conserved. So,
Example: A step transformer is used to convert 120V to 1.50x10^4 V. If the primary coil has 24 turns, how many turns does the secondary coil have?
Example: A step-up transformer has 1000 turns on its primary coil and 1x10^5 turns on its secondary coil. If the transformer is connected to a 120 V power line, what is the step-up voltage?
Example: A step-down transformer reduces the voltage from a 120 V to 12.0 V. If the primary coil has 500 turns and draws 3.00x10-2^ A, a) What is the power delivered to the secondary coil?
b) What is the current in the secondary coil?
