22.6 The Hall Effect

Nuclear fusion is being studied with the goal of economical production of energy by tokamaks.

The device has magnetic fields that direct the charged particles.

Many mass spectrometers use magnetic fields to measure mass.

Mass information can be obtained by measuring the path of a charged particle in the field.
Mass spectrometers and gas chromatographs are used to determine the make-up of large biological molecules.

The effects of a magnetic field on free- moving charges have been seen.

The conductor's charges are affected by the magnetic field.

The Hall effect has important implications.

The figure shows what happens when charges move through a conductor.

The field is related to the width of the conductor.
The conventional current is to the right in both parts of the figure.

The electrons move to the left.

Positive charges move the current to the right.

electrons feel a magnetic force towards one side of the conductor, leaving a net positive charge on the other side

The Hall emf is caused by the magnetic field that is out of the page, represented by circled dots.

The Hall effect can be used to determine the sign of the charge carriers if the direction of the field is known.

The Hall effect can be used to determine whether positive or negative charges carry the current.

The Hall effect shows that electrons carry current in metals and that positive charges carry current in some electronics.
The Hall effect is used to investigate the movement of charges and their densities in materials.
The Hall effect is an example of quantum behavior.

Blood flow rate is one of the uses of the Hall effect.

We need an expression for the Hall emf across a conductor to examine these quantitatively.
The magnetic force can move negative charges to one side, but they can't build up without a limit.
The electric field caused by their separation grows to equal the magnetic force.

The electric field is uniform across the conductor, as is the magnetic field.

The Hall emf is the relationship between the electric field and the voltage.

Where is the Hall effect voltage across a conductor of width through which charges move at a speed?

The Hall emf balances the magnetic force on moving charges with an electric force.

The equilibrium is quickly reached when charge separation builds up until it is balanced by the electric force.

Magnetic field strength is one of the most common uses of the Hall effect.

Hall probes can be made very small, allowing fine position mapping.
Carefully calibrating hall probes can make them very accurate.
The Hall effect can be used to measure fluid flow in fluid with no charges.
The Hall emf is produced by a magnetic field applied to the flow direction.
The magnitude of the Hall emf is what the pipe diameter is, so that the average velocity can be determined.

The Hall effect can be used to measure fluid flow.

The Hall emf is proportional to the average velocity and is measured across the tube.

A Hall effect flow probe is placed on an arteries and applied with a 0.100-T magnetic field.

The equation can be used to find.

This is the average output.

The instantaneous voltage changes with the blood flow.
The measurement has a small voltage.
The Hall emf is AC with the same frequencies if an AC magnetic field is applied.
An amplifier can pick out the right frequencies, eliminating signals and noise from other frequencies.

Magnetic force on charges moving in a conductor is transmitted to the conductor itself.

The same direction as that on the individual moving charges is given by the right hand rule 1 when the magnetic field exerts a force on a current-carrying wire.

The force can be large enough to move the wire because of the large number of moving charges.

Taking a sum of the magnetic forces on individual charges can be used to derive an expression for the magnetic force on a current.

The force on an individual charge is given.

Taking to be uniform over a length of wire and zero elsewhere, the total magnetic force on the wire is then, where is the number of charge carriers in the section of wire of length.

The force on the wire is determined by where the cross-sectional area of the wire is.

22.16 is the equation for magnetic force on a length of wire carrying a current in a uniform magnetic field.

The direction of this force is given by RHR-1, with the thumb in the direction of the current.

RHR-1 gives its direction.

A large magnetic field creates a force on a small length of wire.

Magnetic force on current-carrying conductors converts electric energy to work.

Magnetic force pumps fluids without moving mechanical parts is a clever application.

The magnetic force on the current can be used as a non mechanical pump.

A strong magnetic field is applied across a tube and a current is passed through the fluid at right angles to the field, resulting in a force on the fluid parallel to the tube axis as shown.

The absence of moving parts makes it attractive to move a hot substance in a nuclear reactor.
Experimental artificial hearts are testing out this technique for pumping blood, possibly circumventing the adverse effects of mechanical pumps.

Nuclear submarines have the ability to hide and survive a first or second nuclear strike.

Development work is needed for existing MHD drives.

The MHD system in a nuclear submarine would allow it to run more silently and produce less turbulence than propellers.

The Hunt for Red October dramatized the development of a silent drive submarine.

There are loops of wire in the magnetic field.

The magnetic field exerts Torque on the loops when current is passed through them.
The mechanical work is done with electrical energy.

A loop of wire attached to a rotating shaft feels magnetic forces that produce a clockwise Torque as seen from above.

The magnetic field is uniform over the rectangular loop.

The forces on the top and bottom segments are parallel to the shaft, so there is no Torque.
There is no net force on the loop because the vertical forces are equal in magnitude and opposite in direction.
Torque is defined as where the force is applied, the distance from the pivot that the force is applied, and the angle between and.

The clockwise Torque is produced by each force.

The two add to give a total Torque, since the Torque on each vertical segment is.

The angle between and the field is the same as the angle between and the loop.

The force on each segment is determined by the length of the segment.

We get times the Torque of one loop if we have a multiple loop of turns.

There is a magnetic field and a current-carrying loop.

The equation can be used for a loop of any shape.
The loop carries a current, has turns, each of the area, and the loop makes an angle with the field.
The loop has zero net force.

The maximum Torque can be found on a 100 turn square loop of a wire with a side carrying 15.0 A of current.

Torque can be found using the loop.

It's large enough to be useful in a motor.

The maximum is what was found in the preceding example.

The coil's Torque decreases to zero as it rotates.
Once the coil rotates past, the Torque reverses its direction.
Unless we do something, the coil will move back and forth about equilibrium.
We can reverse the current with brushes if we want the coil to continue rotating in the same direction.

The figure's meter has magnets shaped to limit the effect of the loop over a large range.

The Torque is proportional to something.
A linear spring balances the current produced Torque.
The needle is proportional to.
The gauge reading can be adjusted if an exact proportionality cannot be achieved.
We use a large loop area, high magnetic field, and low-resistance coil to make a galvanometer for use in ammeters that have a low resistance and respond to small currents.

Meters are very similar to a motor, but only move through a part of a revolution.

The magnetic poles of this meter are shaped so that the component of the loop constant is not dependent on the current.

Magnetic fields created by overhead electric power lines can interfere with compass readings.

When Oersted discovered that a current in a wire affected a compass needle, he was not dealing with large currents.
The law governing the fields created by currents is discussed in this section.

There are both direction and magnitude magnetic fields.

The magnitude of the field can be determined by hall probes.
There is a field around a long wire.

The rule is in line with the field mapped for the long straight wire.

The magnitude of the field is dependent on distance from the wire and not on position along the wire.

A magnetic field twice the strength of the Earth's would be created by finding the current in a long straight wire.

Due to the wire, the Earth's field is taken to be.

Since all other quantities are known, the equation can be used to find it.

A large current produces a magnetic field that is close to a long straight wire.

Since the Earth's field is specified to only two digits, the answer is stated to only two digits.

You might think that the magnetic field of a long straight wire is inconsequential.

The total field of any shape current is the sum of the fields due to each segment.
The field needs to be summed for an arbitrary shape current.
The realization that electric and magnetic fields are different manifestations of the same thing led to the modern theory of relativity.
The amount of space that can be devoted to it is beyond the scope of the text.
For the interested student, and particularly for those who continue in physics, engineering, or similar fields, looking into these matters further will reveal descriptions of nature that are elegant as well as profound.
We will keep the general features in mind, such as RHR-2 and the rules for magnetic field lines listed in Magnetic Fields and Magnetic Field Lines, while focusing on the fields created in certain important situations.

Sometimes we get the impression that Einstein invented something when we hear about him.

Einstein's motivation was to solve difficulties in knowing how different observers see magnetic and electric fields.

The direction and magnitude of the magnetic field produced by a current-carrying loop are complexample RHR-2 can be used to give the direction of the field near the loop, but mapping with compasses and the rules about field lines given in Magnetic Fields and Magnetic Field Lines are needed.

Where is the loop located?

The equation is very similar to one for a straight wire, but only valid at the center of the loop of wire.
Field strength can be obtained at the center of a loop if the equations are similar.
One way to get a larger field is to have loops.
The larger the loop, the smaller the field at its center.

The field is similar to a bar.

The field inside a solenoid can be very strong because of its shape.

The field is very cold.

The field is very cold.

The magnetic field inside of a current-carrying solenoid is very uniform.

Only near the end does it begin to weaken and change direction.

The field strength is not only at the center, but also in the uniform region of the interior.

Large uniform fields can be spread over a large volume with solenoids.

The field strength is found by using.

This is a large field strength that can be established over a large-diameter solenoid.

The fields of this strength are not easy to achieve.

A large current through 1000 loops squeezing into a meter's length would produce significant heating.

Superconducting wires can be used to achieve higher currents.
There is an upper limit to the current since the state is disrupted by large magnetic fields.

There are many variations of the flat coil.

The toroidal coil used to confine the particles in tokamaks is similar to a solenoid bent into a circle.
The field inside a toroid is very strong.
The charged particles travel in circles and collide with one another.
The charged particles don't cross field lines.
Magnetic field shapes can be produced with a range of coil shapes.
Adding ferromagnetic materials can have a significant effect on the shape of the field.

The Earth's magnetic field is adversely affected by magnetic fields in ferromagnetic materials and they are used as shields for devices that are adversely affected.

You can learn how to make a bulb light using magnets.

Since ordinary currents produce magnetic fields and these fields exert significant forces on ordinary currents, you might expect that there are significant forces between wires.

The force between wires is not used to define the ampere.
This force has something to do with why large circuit breakers burn up when they attempt to interrupt large currents.

The force between two conductors separated by a distance can be found by applying what we have developed in preceding sections.

Let's consider the field produced by wire 1 and the force it exerts on wire 2.

When the currents are in the same direction, the force between the parallel conductors is attractive.

The force between the currents is repulsive.

The forces on the wires are equal in magnitude, and so we just write for the magnitude.

The force per unit length is convenient since the wires are long.

The force per unit length between two parallel currents is 22.32.

The force is attractive if the currents are both repulsive and in the same direction.

The pinch effect is caused by this force.

Whether the currents are in wires or not, the force exists.
An attraction that squeezes currents into a smaller tube is found in an electric arcs.
The pinch effect can cause an arcs between plates of a switch trying to break a large current, burn holes, and even ignite the equipment.

There are jets of ionized material, such as solar flares, that are shaped by magnetic forces.

The definition of the ampere is based on the force between wires.

The force per meter is exactly what it is.

The operational definition of the ampere is based on this.