We learned in Chapter 8 that electric currents can generate magnetic fields.
Magnetic fields are generated by moving charges.
Magnetic fields can generate moving charges or current.
The figure below shows a wire moving with a uniform magnetic field B that's parallel to the page.
The moving electrons in the wire are affected by the magnetic field.
With B pointing into the page, the direction of v is to the right, so the magnetic force, F B, for positive charges, would be upward by the right-hand rule.
In order to find the direction of current, you will have to use a combination of your right-hand rules.
Pay attention to orientation.
An excess of positive charge will be left at the upper end of the wire because electrons will be pushed to the lower end.
A uniform electric field is created by the separation of charge.
A charge in the wire feels two forces: an electric force and a magnetic force.
If q is positive, F E is upward and F B is downward.
The charges in the wire are in equilibrium if the magnitude of F E equals the magnitude of F B.
This happens when qE is qvB and E is vB.
A potential difference between the ends of the rod is created by the electric field.
Negative charge accumulates at the lower end and positive charge accumulates at the upper end, so point b is at a higher electric potential.
Since E is vB, the potential difference can be written as vBl.
Imagine that the rod is sliding along a pair of rails connected to the left by a bar.
The potential difference Vba causes current to flow as the sliding rod completes a rectangular circuit.
In the next section, we will see how each of the three changes causes a change in the flux.
The magnetic field exerts a force on the sliding rod when there is a current in it.
The direction of F B on the rod is indicated by the fact that l points upward in the direction of the current.
An external agent needs to give the same amount of force to the right to keep the current flowing.
The power and electrical power delivered to the circuit are determined by the power supplied by the external agent.
The two expressions are the same.
The energy provided by the external agent is turned into electrical and thermal energy by the conductors that make up the circuit.
The basis for Faraday's Law can be found in the relationship between current in a coil of wire and magnetic fields.
A magnetic field can be used to create an emf, but there is another way to do it.
When the magnetic flux passes through the coil or loop of wire, a current is created.
The amount of field passing into the loop is defined by magnetic flux.
The amount of air that flows through the loop depends on a number of factors.
In the situation to the left, the most effective airflow is when the loop is completely parallel.
When the loop is in the situation to the right, it is the least effective.
This idea can be applied to a magnetic field.
The product of A and the magnetic field parallel to the area are equal to the magnetic flux through an area A.
The density of magnetic field lines is measured.
The figure below shows two views of a circular loop of 3 cm placed within a magnetic field.
The weber (Wb) is equivalent to one Tm 2 and is the SI unit for Magnetic Flux.
The weber is the SI unit for the tesla*meter 2.
The concept of magnetic flux is important.
The magnitude of the emf in a circuit is the same as the rate of change of the magnetic flux through the circuit.
This emf can create a magnetic field.
The direction of the current is determined by the direction in which the emf is travelling.
If this were not the case, the magnetic flux created by the current would amplify the change that produced it, and energy would not be saved.
To oppose this change, we would need to make some magnetic waves.
The right-hand rule tells us that the current would produce a magnetic field if it was in the counterclockwise direction.
The current will flow only when the loop rotates.
The current will disappear if the loop rotates 45 degrees.
Because the area is changing, the magnetic flux through the loop will change, which will cause an emf in the loop.
We can figure out the direction of the current.
As the rod moves to the right, the page gets more magnetic.
The out-of-the-page flux was produced.
The current must be counterclockwise in order to generate a magnetic field that points out of the plane of the page.
The magnitude of the emf and direction of the current agree with the results we got in the section on motional emf.
This example shows how a violation of Lenz's Law could lead to a violation of the Law ofConservation of Energy.
The current in the sliding rod is directed upward so that the electrons drift downward.
The force that's pulling the rod to the right is directed to the left by the force that's directing the electrons to the left.
If the current were directed downward, the magnetic force on the rod would be to the right, causing the rod to accelerate to the right with an equal amount of energy from an external agent.
A magnetic field can be created by a permanent magnet.
The current generated by the emf will oppose the change.
A square loop of wire 2 cm on each side has a total resistance of zero.
It is placed 20 cm from the wire.
Determine the magnitude and direction of the current in the square loop if the current in the straight wire is increased at a steady rate from 20 A to 50 A in 2 s.
The strength of the magnetic field is determined by the equation B, which shows that the magnetic field is directed out of the plane of the page.
As the current in the straight wire increases, the magnetic flux through the turns of the square loop changes, inducing an emf and current.
The total flux is the number of loops N times the number of individual loops, ph B.
As the current in the straight wire increases, the magnetic flux through the loop goes out of the page.
An into-the-page magnetic field can be generated by opposing an increasing out-of-the-page flux.
Chapter 12 contains solutions.
A uniform magnetic field B points out the plane of the page as a metal rod of length L is pulled upward.
A conducting rod of length 0.2 m and resistance 10 ohms between its endpoints does not slide along a U-shaped conductor in a uniform magnetic field B of magnitude 0.5 T to the plane of the conductor, as shown in the diagram below.
In the figure below, a small loop of wire is placed on a stand inside a hollow solenoid.
The counterclockwise current I is carried by the solenoid, which has n turns per unit length.
If the current in the solenoid is decreased at a steady rate, you can determine the direction of the current in the loop.
A permanent bar magnet is below a loop of wire.
It is pulled upward through a loop of wire.
A square loop of wire surrounds a long, straight wire that goes through the center of the square.
Determine the current in the square loop if the current in the wire is I.
A wire is pulled through a magnetic field into a page.
The Resistor has a resistance of 20.
As the magnetic field changes, an electric force is produced.
The idea is summarized by Blv.
The amount of magnetic field goes through a surface.
The strength of the magnetic field, the surface area through which the field passes, and the angle between the two are some of the factors that affect the magnetic flux.
The idea is summed up by phB.
If the wire is formed in a loop, the magnetic force will change with time.