Showing posts with label ELECTROMAGNETICS. Show all posts
Showing posts with label ELECTROMAGNETICS. Show all posts

## Magnetic force on a current carrying wire virtual experiment

#### Quiz

Q1) The force on a moving charge in the presence of a magnetic field is always

A. Perpendicular to both the charge's velocity and the magnetic field
B. Parallel to the charge's velocity
C. Parallel to the magnetic field
D. None of the above

Q2)  A current is moving from north to south through a long wire that is lying horizontally on a table. What is the direction of the magnetic force if the magnetic field is directed up and out of the table?

A. toward the north
B. toward the east
C. toward the south
D. toward the west

#### Magnetic force on a current carrying wire Simulation(Virtual Experiment)

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Magnetic force on a current carrying wire
If a magnetic field exerts a force on a single charged particle when it moves through a magnetic field, it should be no surprise that magnetic forces are exerted on a current-carrying wire as well (see Fig. 1). Because the current is a collection of many charged particles in motion, the resultant force on the wire is due to the sum of the individual forces on the charged particles. The force on the particles is transmitted to the “bulk” of the wire through collisions with the atoms making up the wire.

FIGURE 1 This apparatus demonstrates the force on a current carrying wire in an external magnetic field. Why does the bar swing away from the magnet after the switch is closed?

Some explanation is in order concerning notation in many of the figures. To indicate the direction of $\ B$, we use the following conventions:

 If $\ B$ is directed into the page, as in Figure 2, we use a series of green crosses, representing the tails of arrows. If $\ B$ is directed out of the page, we use a series of green dots, representing the tips of arrows. If $\ B$ lies in the plane of the page, we use a series of green field lines with arrowheads.

The force on a current-carrying conductor can be demonstrated by hanging a wire between the poles of a magnet, as in Figure 2. In this figure, the magnetic field is directed into the page and covers the region within the shaded area. The wire deflects to the right or left when it carries a current.

FIGURE 2  A segment of a flexible vertical wire partially stretched between the poles of a magnet, with the field (green crosses) directed into the page. (a) When there is no current in the wire, it remains vertical. (b) When the current is upward, the wire deflects to the left. (c) When the current is downward, the wire deflects to the right.

Magnetic Force on a wire resulting from a magnetic field
It is possible to determine the force of magnetism exerted on a current-carrying wire passing through a magnetic field at right angles to the wire. Experiments show that the magnitude of the force, $\ F$, on the wire, is proportional to the strength of the field, $\ B$, the current, $\ I$, in the wire, and the length, $\ L$, of the wire in the magnetic field. The relationship of these four factors is as follows:

 Magnetic Force on a Current-Carrying Wire in a Magnetic Field  $\ F=BIL$ The force on a current-carrying wire in a magnetic field is equal to the product of magnetic field strength, the current, and the length of the wire.

The strength of a magnetic field, $\ B$, is measured in teslas, T. 1T is equivalent to 1 N/A m.
Note that if the wire is not perpendicular to the magnetic field, a factor of $\sin \theta$ is introduced in the above equation, resulting in $\ F=BILsin \theta$ . As the wire becomes parallel to the magnetic field, the angle becomes zero, and the force is reduced to zero. When $\theta$=90°, the equation is again $\ F=BIL$.

Determining the Magnetic force’s direction
Faraday’s description of the force on a current-carrying wire does not completely describe the direction because the force can be upward or downward. The direction of the force on a current carrying wire in a magnetic field can be found by using the third right-hand rule. This technique is illustrated in Figure 3. The magnetic field is represented by the symbol B, and its direction is represented by a series of arrows. To use the third right-hand rule, point the fingers of your right hand in the direction of the magnetic field, and point your thumb in the direction of the conventional (positive) current in the wire.

Figure 3 The third right-hand rule can be used to determine the direction of force when the current and magnetic field are known.

The palm of your hand will be facing in the direction of the force acting on the wire. When drawing a directional arrow that is into or out of the page, direction is indicated with crosses and dots, respectively. Think of the crosses as the tail feathers of the arrow, and the dots as the arrowhead.

## Superposition principle of electric field virtual experiment

#### Quiz

Q1) A has a charge of +2 µC, and object B has a charge of +6 µC. Which statement is true:

A. $\ F_{AB}$= $\ –3F_{BA}$
B. $\ F_{AB}$=$\ –F_{BA}$
C. $\ 3F_{AB}$=$\ –F_{BA}$

By Newton’s third law, the two objects will exert forces having equal magnitudes but opposite directions on each other.

Q2) At the position of the dot, the electric field points

A. Up.
B. Down.
C. Left.
D. Right.
E. The electric field is zero.

The direction of the field is taken to be the direction of the force it would exert on a positive test charge

#### Superposition principle of electric fields Simulation(Virtual Experiment)

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Force, Charges, and Distance
The electrical force between any two objects obeys a similar inverse-square relationship with distance. The relationship among electrical force, charges, and distance, now known as Coulomb’s law, was discovered by the French physicist Charles Coulomb (1736–1806) in the eighteenth century. Coulomb’s law states that for charged particles or objects that are small compared with the distance between them, the force between the charges varies directly as the product of the charges and inversely as the square of the distance between them.

Coulomb’s law can be expressed as

$\ F = k \frac {q_{A}q_{B}}{d^2}$

where $\ d$ is the distance between the charged particles; $\ q_{A}$ represents the quantity of charge of one particle and $\ q_{B}$the quantity of charge of the other particle; and $\ k$ is the proportionality constant.

When the charges are measured in coulombs, the distance is measured in meters, and the force is measured in newtons, the constant, K, is $\ 9.0 X 10^9 N m^2/C^2$.
This equation gives the magnitude of the force that charge $\ q_{A}$ exerts on $\ q_{B}$ and also the force that $\ q_{B}$ exerts on $\ q_{A}$. These two forces are equal in magnitude but opposite in direction. You can observe this example of Newton’s third law of motion in action when you bring two strips of tape with like charges together. Each exerts forces on the other. If you bring a charged comb near either strip of tape, the strip, with its small mass, moves readily. The acceleration of the comb and you is, of course, much less because of the much greater mass.
The electrical force, like all other forces, is a vector quantity. Force vectors need both a magnitude and a direction. However, Coulomb’s law will furnish only the magnitude of the force. To determine the direction, you need to draw a diagram and interpret charge relations carefully.
Consider the direction of force on a positively charged object called A. If another positively charged object, B, is brought near, the force on A is repulsive. The force, $\ F_{B}$ on A, acts in the direction from B to A, as shown in Figure 1a. If, instead, B is negatively charged, the force on A is attractive and acts in the direction from A to B, as
shown in Figure 1b.

FIGURE 1 The rule for determining direction of force is like charges repel, unlike charges attract.

The superposition principle
• The electric force obeys the superposition principle.
• That means the force two charges exert on a third force is just the vector sum of the forces from the two charges, each treated without regard to the other charge.
• The superposition principle makes it mathematically straightforward to calculate the electric forces exerted by distributions of electric charge.
• The net electric force is the sum of the individual forces.

The Electric Field
The electric field is a vector quantity that relates the force exerted on a test charge to the size of the test charge. How does this work? An electric charge, q, produces an electric field that you can measure. This is shown in Figure 2. First, measure the field at a specific location.

FIGURE 2 Arrows can be used to represent the magnitude and direction of the electric field about an electric charge at various locations.

Call this point A. An electrical field can be observed only because it produces forces on other charges, so you must place a small positive test charge, $\ q′$, at A. Then, measure the force exerted on the test charge, $\ q′$, at this location.
According to Coulomb’s law, the force is proportional to the test charge. If the size of the test charge is doubled, the force is doubled.
Thus, the ratio of force to test charge is independent of the size of the test charge. If you divide the force, F, on the test charge, measured at point A, by the size of the test charge, $\ q′$, you obtain a vector quantity, $\ F/q$′. This quantity does not depend on the test charge, only on the charge q and the location of point A. The electric field at point A, the location of $\ q′$, is represented by the following equation.

Electric Field E

$\ E = \frac {F_{on q'}}{q'}$
$\ E = k\frac {q}{r^2}$.....[single point charge q]

The direction of the electric field is the direction of the force on the positive test charge. The magnitude of the electric field is measured in newtons per coulomb, N/C.
A picture of an electric field can be made by using arrows to represent the field vectors at various locations, as shown in Figure 2.

The length of the arrow will be used to show the strength of the field. The direction of the arrow shows the field direction. To find the field from two charges, the fields from the individual charges are added vectorially. A test charge can be used to map out the field resulting from any collection of charges.

Superposition principle of electric fields
The superposition principle states that, for a collection of charges, the total electric field at a point is simply the summation of the individual fields due to each charge

 at any point P, the total electric field due to a group of charges equals the vector sum of the electric fields of the individual charges.

The dipole: an important charge distribution
• An electric dipole consists of two point charges of equal magnitude but opposite signs, held a short distance apart.

## Faraday’s Law and Lenz's Law Electromagnetic Induction Simulation

#### Quiz

A. an emf is induced in a loop when it moves through an electric field
B. the induced emf produces a current whose magnetic field opposes the original change
C. the induced emf is proportional to the rate of change of magnetic flux

Q2)  If a coil is shrinking in a B field pointing into the page, in what direction is the induced current?

A. clockwise
B. counter-clockwise
C. no induced current

Downward flux is decreasing, so need to create downward B field.

#### Faraday’s Law Electromagnetic Induction Simulation(Virtual Experiment)

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Faraday and Henry both made the same discovery. Electric current can be produced in a wire by simply moving a magnet into or out of a wire coil. No battery or other voltage source was needed only the motion of a magnet in a coil or in a single wire loop as shown in Figure 1.

FIGURE 1. When the magnet is plunged into the coil, voltage is induced in the coil and charges in the coil are set in motion.

They discovered that voltage was induced by the relative motion of a wire with respect to a magnetic field. The production of voltage depends only on the relative motion of the conductor with respect to the magnetic field. Voltage is induced whether the magnetic field of a magnet moves past a stationary conductor, or the conductor moves through a stationary magnetic field as shown in Figure 2. The results are the same for the same relative motion.

FIGURE 2. Voltage is induced in the wire loop whether the magnetic field moves past the wire or the wire moves through the magnetic field.

To see how an emf can be induced by a changing magnetic field, consider a loop of wire connected to a sensitive ammeter, as illustrated in Figure 3. When a magnet is moved toward the loop, the galvanometer needle deflects in one direction, arbitrarily shown to the right in Figure 3a. When the magnet is brought to rest and held stationary relative to the loop (Fig. 3b), no deflection is observed. When the magnet is moved away from the loop, the needle deflects in the opposite direction, as shown in Figure 3c. Finally, if the magnet is held stationary and the loop is moved either toward or away from it, the needle deflects. From these observations, we conclude that the loop detects that the magnet is moving relative to it and we relate this detection to a change in magnetic field. Thus, it seems that a relationship exists between current and changing magnetic field.
These results are quite remarkable in view of the fact that a current is set up even though no batteries are present in the circuit! We call such a current an induced current and say that it is produced by an induced emf.

Figure 3 (a) When a magnet is moved toward a loop of wire connected to a sensitive ammeter, the ammeter deflects as shown, indicating that a current is induced in the loop. (b) When the magnet is held stationary, there is no induced current in the loop, even when the magnet is inside the loop. (c) When the magnet is moved away from the loop, the ammeter deflects in the opposite direction, indicating that the induced current is opposite that shown in part (a). Changing the direction of the magnet’s motion changes the direction of the current induced by that motion.

Now let us describe an experiment conducted by Faraday and illustrated in Figure 4. A primary coil is connected to a switch and a battery. The coil is wrapped around an iron ring, and a current in the coil produces a magnetic field when the switch is closed. A secondary coil also is wrapped around the ring and is connected to a sensitive ammeter. No battery is present in the secondary circuit, and the secondary coil is not electrically connected to the primary coil. Any current detected in the secondary circuit must be induced by some external agent.

Initially, you might guess that no current is ever detected in the secondary circuit. However, something quite amazing happens when the switch in the primary circuit is either opened or thrown closed. At the instant the switch is closed, the galvanometer needle deflects in one direction and then returns to zero. At the instant the switch is opened, the needle deflects in the opposite direction and again returns to zero.

Figure 4. Faraday’s experiment. When the switch in the primary circuit is closed, the ammeter in the secondary circuit deflects momentarily. The emf induced in the secondary circuit is caused by the changing magnetic field through the secondary coil.

Finally, the galvanometer reads zero when there is either a steady current or no current in the primary circuit. The key to understanding what happens in this experiment is to first note that when the switch is closed, the current in the primary circuit produces a magnetic field in the region of the circuit, and it is this magnetic field that penetrates the secondary circuit. Furthermore, when the switch is closed, the magnetic field produced by the current in the primary circuit changes from zero to some value over some finite time, and this changing field induces a current in the secondary circuit.

As a result of these observations, Faraday concluded that an electric current can be induced in a circuit (the secondary circuit in our setup) by a changing magnetic field. The induced current exists for only a short time while the magnetic field through the secondary coil is changing. Once the magnetic field reaches a steady value, the current in the secondary coil disappears. In effect, the secondary circuit behaves as though a source of emf were connected to it for a short time. It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field.
The experiments shown in Figures 3 and 4 have one thing in common: in each case, an emf is induced in the circuit when the magnetic flux through the circuit changes with time. In general,

The emf induced in a circuit is directly proportional to the time rate of change of the magnetic flux through the circuit.

This statement, known as Faraday’s law of electromagnetic induction, can be written

 Faraday’s Law $\ E = -N \frac {d\Phi_{B}}{dt}$ where $\Phi_{B} =\int \mathbf{B}\cdot d\mathbf{A}$ is the magnetic flux through the circuit in N loops.

Lenz’s Law
The SI unit for the induced emf is the volt, V. The minus sign in the above Faraday’s law of induction is due to the fact that the induced emf will always oppose the change. It is also known as the Lenz’s law and it is stated as follows,

 Lenz’s Law The current from the induced emf will produce a magnetic field, which will always oppose the original change in the magnetic flux.

## Two Bar Magnet Magnetic Field Lines Simulation

#### Quiz

Q1) The force between two unlike magnetic poles

A. increases linearly with the separation distance between them
B. increases as the square of the separation distance between them
C. decreases as the separation distance between them
D. decreases as the square of the separation distance between them

Q2)  An iron rod becomes magnetic when.

a. positive ions accumulate at _me end and negative ions at the other end.
b. its atoms are aligned having plus charges on one side and negative charges on the other.
c. the net spins of its electrons are in the same direction.
d. its electrons stop moving and point in the same direction.
e. none of these.

#### Two Bar Magnet Magnetic Field Lines Simulation(virtual experiment)

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Magnetic Fields Around Permanent Magnets
When you experimented with two magnets, you noticed that the forces between magnets, both attraction and repulsion, occur not only when the magnets touch each other, but also when they are held apart. In the same way that long-range electric and gravitational forces can be described by electric and gravitational fields, magnetic forces can be described by the existence of fields around magnets. These magnetic fields are vector quantities that exist in a region in space where a magnetic force occurs.

Figure 1 The magnetic field of a bar magnet shows up clearly in three dimensions when the magnet is suspended in glycerol with iron filings (a). It is, however, easier to set up a magnet on a sheet of paper covered with iron filings to see the pattern in two dimensions (b).

The presence of a magnetic field around a magnet can be shown using iron filings. Each long, thin, iron filing becomes a small magnet by induction.
Just like a tiny compass needle, the iron filing rotates until it is parallel to the magnetic field. Figure 1a shows filings in a glycerol solution surrounding a bar magnet. The three-dimensional shape of the field is visible. In Figure 1b, the filings make up a two-dimensional plot of the field, which can help you visualize magnetic field lines. Filings also can show how the field can be distorted by an object.

Magnetic field lines
Note that magnetic field lines, like electric field lines, are imaginary. They are used to help us visualize a field, and they also provide a measure of the strength of the magnetic field. The number of magnetic field lines passing through a surface is called the magnetic flux. The flux per unit area is proportional to the strength of the magnetic field. As you can see in Figure 1, the magnetic flux is most concentrated at the poles; thus, this is where the magnetic field strength is the greatest. The direction of a magnetic field line is defined as the direction in which the north pole of a compass points when it is placed in the magnetic field. Outside the magnet, the field lines emerge from the magnet at its north pole and enter the magnet at its south pole, as illustrated in Figure 2. What happens inside the magnet?

Figure 2 Magnetic field lines can be visualized as closed loops leaving the north pole of a magnet and entering the south pole of the same magnet.

There are no isolated poles on which field lines can start or stop, so magnetic field lines always travel inside the magnet from the south pole to the north pole to form closed loops.

Figure 3 The magnetic field lines indicated by iron filings on paper clearly show that like poles repel (a) and unlike poles attract (b). The iron filings do not form continuous lines between like poles. Between a north and a south pole, however, the iron filings show that field lines run directly between the two magnets.

What kinds of magnetic fields are produced by pairs of bar magnets? You can visualize these fields by placing two magnets on a sheet of paper, and then sprinkling the paper with iron filings. Figure 3a shows the field lines between two like poles. In contrast, two unlike poles (north and south) placed close together produce the pattern shown in Figure 3b. The filings show that the field lines between two unlike poles run directly from one magnet to the other.

Forces on objects in magnetic fields
Magnetic fields exert forces on other magnets. The field produced by the north pole of one magnet pushes the north pole of a second magnet away in the direction of the field line. The force exerted by the same field on the south pole of the second magnet is attractive in a direction opposite the field lines. The second magnet attempts to line up with the field, just like a compass needle.
When a sample made of iron, cobalt, or nickel is placed in the magnetic field of a permanent magnet, the field lines become concentrated within the sample. Lines leaving the north pole of the magnet enter one end of the sample, pass through it, and leave the other end. Thus, the end of the sample closest to the magnet’s north pole becomes the sample’s south pole, and the sample is attracted to the magnet.

## A Bar Magnet Magnetic Field Lines Simulation(Virtual Experiment)

#### Quiz

Q1) The magnetic field lines of a bar magnet

A. begin on a north pole and end on a north pole
B. begin on a south pole and end on a south pole
C. begin on a north pole and end on a south pole
D. begin on a south pole and end on a north pole

Q2)  When I cut a magnet into two pieces I get

A. An isolated north and south magnetic pole
B. Two smaller magnets
C. The two pieces are no longer magnets

#### Bar Magnet Magnetic Field Lines Simulation(Virtual Experiment)

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Magnetic Fields
Place a sheet of paper over a bar magnet and sprinkle iron filings on the paper. The filings will tend to trace out an orderly pattern of lines that surround the magnet. The space around a magnet, in which a magnetic force is exerted, is filled with a magnetic field. The shape of the field is revealed by magnetic field lines. Magnetic field lines spread out from one pole, curve around the magnet, and return to the other pole, as shown in Figure 1.

FIGURE 1. Iron filings trace out a pattern of magnetic field lines in the space surrounding the magnet.

Magnetic Field lines
Magnetic fields exist in three dimensions surrounding a magnet and are more intense at the poles. Magnetic fields are invisible, but can be represented in diagrams with magnetic field lines. Magnetic field lines

• point from the north pole to the south pole outside a magnet, and from the south pole to the north pole inside a magnet
• never cross one another
• are closer together where the magnetic field is stronger

Drawing Field lines
A compass can be used to map the direction of the field lines around a magnet. The compass needle will align itself along the direction of the field. Figure 2 shows the field lines around different magnets.

Figure 2 (a) A magnetic field around a bar magnet with mini compasses on the field lines, (b) A magnetic field around a horseshoe magnet with mini compasses on the field lines, (c) A magnetic field around Earth with mini compasses on the field lines

## Complex Resistor Combinations Simulation

#### Quiz

Q1) You have three 100 resistors available. How would you connect these three resistors to produce a 150 equivalent resistance? You must use all of the resistors.

A. Connect all three resistors in parallel.
B. Connect all three resistors in series.
C. Connect one resistor in series with two resistors in parallel.
D. Connect two resistors in series with the third resistor in parallel to the first two.

Q2)  A circuit is constructed as follows: four resistors in parallel connected in series with three resistors in parallel connected in series with two resistors in parallel. All of the resistors have the same value. How does the equivalent resistance of this circuit compare to the resistance of a single resistor?

A. The equivalent resistance is less than a single resistor.
B. The equivalent resistance is the same as a single resistor.
C. The equivalent resistance is greater than a single resistor.
D. The equivalent resistance cannot be determined without the resistance value of a single resistor.

#### Resistors in parallel total resistance Simulation

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RESISTORS COMBINED BOTH IN PARALLEL AND IN SERIES
Series and parallel circuits are not often encountered independent of one another. Most circuits today employ both series and parallel wiring to utilize the advantages of each type.
A common example of a complex circuit is the electrical wiring typical in a home. In a home, a fuse or circuit breaker is connected in series to numerous outlets, which are wired to one another in parallel. An example of a typical household circuit is shown in Figure 1.

Figure 1. (a) When all of these devices are plugged into the same household circuit, (b) the result is a parallel combination of resistors in series with a circuit breaker.

As a result of the outlets being wired in parallel, all the appliances operate independently; if one is switched off, any others remain on.Wiring the outlets in parallel ensures that an identical potential difference exists across any appliance.
This way, appliance manufacturers can produce appliances that all use the same standard potential difference.
To prevent excessive current, a fuse or circuit breaker must be placed in series with all of the outlets. Fuses and circuit breakers open the circuit when the current becomes too high. A fuse is a small metallic strip that melts if the current exceeds a certain value. After a fuse has melted, it must be replaced. A circuit breaker, a more modern device, triggers a switch when current reaches a certain value. The switch must be reset, rather than replaced, after the circuit overload has been removed. Both fuses and circuit breakers must be in series with the entire load to prevent excessive current from reaching any appliance. In fact, if all the devices in Figure 1 were used at once, the circuit would be overloaded. The circuit breaker would interrupt the current.

Fuses and circuit breakers are carefully selected to meet the demands of a circuit. If the circuit is to carry currents as large as 30 A, an appropriate fuse or circuit breaker must be used. Because the fuse or circuit breaker is placed in series with the rest of the circuit, the current in the fuse or circuit breaker is the same as the total current in the circuit. To find this current, one must determine the equivalent resistance.
When determining the equivalent resistance for a complex circuit, you must simplify the circuit into groups of series and parallel resistors and then find the equivalent resistance for each group by using the rules for finding the equivalent resistance of series and parallel resistors.

Work backward to find the current in and potential difference across a part of a circuit Now that the equivalent resistance for a complex circuit has been determined, you can work backward to find the current in and potential difference across any resistor in that circuit. In the household example, substitute potential difference and equivalent resistance in $\Delta V = IR$ to find the total current in the circuit. Because the fuse or circuit breaker is in series with the load, the current in it is equal to the total current. Once this total current is determined, $\Delta V = IR$ can again be used to find the potential difference across the fuse or circuit breaker.

There is no single formula for finding the current in and potential difference across a resistor buried inside a complex circuit. Instead, $\Delta V = IR$ and the rules reviewed in Table must be applied to smaller pieces of the circuit until the desired values are found.