strand h. electromagnetism unit 1. magnets and magnetic fields

Strand H. Electromagnetism Unit 1. Magnets and Magnetic Fields Text Contents Page Magnetic Materials 2 The Magnetic Field of a Bar Magnet 5 The Magnetic Field of Current Carrying Wires 9 Electromagnets 12

Strand H Unit 1: Electromagnetism Text

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H.1.1. Magnetic Materials In the previous strand, electrostatics was discussed and the idea of the electric field introduced. At no point was there a need to discuss magnets or magnetic fields, even though later in this unit we will learn that electric and magnetic fields go hand in hand. This is because the electric field discussion was built around stationary charges. As soon as a charge begins to move through space, either accelerating or at constant velocity, it generates a magnetic field.

Permanent magnets, such as a bar magnet or a fridge magnet, are always magnetic. They are made from magnetic materials. They create a magnetic field around themselves, and they exert a force on other magnets, and also on some materials that are not permanent magnets. There are only a few pure metals that can be used to make a permanent magnet. They are;

• Colbalt • Iron • Nickel

Steel can also be used but it is an alloy of iron, not a pure metal. Other materials can be magnetic when placed in a magnetic field or when they are stroked by a permanent magnet. These materials are soft magnetic materials, and are usually ferrous metals (an alloy containing iron). If you bang, drop, or hit a soft magnet with a hammer it either looses its magnetism, or the strength of the magnet reduces. In order to explain this behavior, and to explain why most materials are non-magnetic, a few (3) are permanently magnetic, and ferrous metals are soft magnetic, we need to consider the atomic structure of the material, and how the materials atoms are arranged. As discussed, magnetism is a direct result of moving charge, and only moving charge. All materials are made of atoms. Around every atom’s core (the nucleus), there are a number of electrons whizzing around at great speeds in spherical orbits called orbitals. It is the movement of these electrons that create a magnetic field, and so all atoms act as tiny individual bar magnets. Each atom possesses a north and a south pole, just like a bar magnet, and the atoms magnetic moment, which is signified by an arrow, points in the direction of the atoms magnetic north pole as shown in Figure H.1.1.1.

Magnetic fields are generated by moving charge

Nucleus Electron

Magnetic Moment

Figure H.1.1.1


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Now consider Figure H.1.1.2. Here we see a small section of a material. In reality, the atoms are arranged in domains, which are tiny fault lines in the structure of the atomic packing, producing ‘islands’ of similarly orientated atoms, but here we will represent each domain pictorially by a single atom. In material (a), the magnetic moments (the magnetic north poles) of the atoms (blue arrows) are arranged randomly. The combined magnetic effect from these randomly orientated atoms cancel each other out, resulting in no overall magnetism. This material is therefore non-magnetic.

In material (b), there is still some degree of randomness to the orientation of the atoms. However, there is an overall orientation, in the direction of the black arrow. The components of the magnetic field from the individual atoms in this orientation reinforce each other, giving a net magnetic response. This material is magnetic, but not strongly so (likely to be a soft magnetic material such as iron). In material (c) the orientation is more pronounced, therefore the net magnetic response is stronger, making a stronger magnet. This material is a strong, or ‘hard’ permanent magnet. In general; This origin of the materials magnetism also explains why some materials can be magnetised or demagnetised. In soft magnetic materials, randomly orientated magnetic moments can be aligned by stroking with a permanent magnet in much the same way as a compass needle lines up with the Earth’s magnetic field, causing the magnetic response of the material to increase. Shocking the material

(a) non-magnetic (b) magnetic (b) strongly magnetic

Figure H.1.1.2

The more the magnetic moments of the atoms in a material are aligned, the stronger the magnet.


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by dropping it or banging it down on hard surface causes these aligned atoms to revert to their original orientations, demagnetising the material. Exercise H.1.1 1. Name the three pure metals that are permanently magnetic. 2. Which type of alloy commonly forms soft magnetic materials? Which pure magnetic material do they contain? 3. Which of the following materials is likely to be a ferrous alloy? Explain your reasoning.

4. For the alloy in question 3, explain how the strength of the magnetic field be increased. Challenge Question 5. A student is given an iron nail, some paper clips, and a permanent magnet. Plan how the student could conduct an experiment to prove the iron nail was a soft magnetic material. Include the likely observations and conclusions that you would expect the student to make.

(a) (b) (c)


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H.1.2. The Magnetic Fields of a Bar Magnet A rectangular block of permanently magnetic material is known as a bar magnet, as shown in Figure H.1.2.1. If the bar magnet were suspended from its center of gravity by a thread, it would act like a compass needle, aligning with the Earth’s magnetic field, and one end of the magnet would point north. The north seeking end of the bar magnet is the north pole (N) and the south seeking end is the south pole, (S). When two bar magnets are arranged such that the poles of each magnet are brought together we find that When a bar magnet is covered with a piece of paper and iron filings (tiny soft magnetic rod shaped shards of iron) are sprinkled on to the paper, the filings align their long axis with the magnetic field (Figure H.1.2.2.). This alignment shows the magnetic field filling the space around the magnet. When another magnet is placed in that field it experiences a force. Note that the filings orientate themselves to form ‘loops’ which seem to terminate at the poles. These lines are the magnetic field lines, sometimes called the lines of force. Figure H.1.2.3. shows a schematic of the field of a bar magnet, with field lines form closed loops, coming from the north pole, to the south pole of the magnet.

Like poles repel and opposite poles attract

N S S N

N S S N

S N S N

F F

F F

F F

Figure H.1.2.1.

Magnetic field lines form closed loops, and have a direction that flows from north to south. When field lines are far apart the field strength B is small. When field lines are close together the field

strength B is large

Figure H.1.2.2.


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On first inspection, this result is very different and yet feels similar to the formation of electric field. Recall that electric fields form lines start on a positive charge and end on a negative charge whilst magnetic field lines flow from north pole to south pole. But electric field lines do not form closed loops. This is because the electric ‘poles’, the positive and negative charges may be separated, and further may exist as a single negative or positive charge. Magnetic poles cannot exist on their own. If we took a very sharp implement and cut the bar magnet in two in order to separate the poles, then a new north and south pole would immediately form and the two fragments would become two separate bar magnets. When unlike poles of two bar magnets A and B face each other, the two magnets attract each other. The magnetic field flows from the north pole of magnet A to the south pole of magnet B and the field between the two magnets is uniform, because the field lines are parallel to each other. When like poles of the two magnets face each other they repel. The field lines between them bend away from each other causing a void of field between the two magnets.

N S

Figure H.1.2.3.

S S N N A B

S S N N A B

Figure H.1.2.4.


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The Earth also has a magnetic field that looks like the field of a giant bar magnet as shown by Figure H.1.2.4. It is this field to which a compass aligns, with the north pole of the compass needle pointing to the magnetic north pole of the Earth. The Earth’s magnetic field is generated by its molten metal core. As the Earth rotates on its axis, it causes circulation currents in the molten iron core at the Earths center. This movement of metal constitutes a large movement of charge, which generates the magnetic field. The Earth’s magnetic field plays a very important role in making the Earth inhabitable to life. The magnetic field deflects harmful charged particles from space and from our own sun. It is these interactions that cause the northern and southern lights (Aurora Borealis and Australis). Without this magnetic ‘umbrella’ we would be bathed in harmful ionising radiation. Exercise H.1.2. 1. Sketch the field of the bar magnet pictured, clearly marking the direction of the field lines. 2. Describe the origin of the Earth’s magnetic field and explain its importance in terms of screening charged particles from space. 3. The following diagram shows a bar magnet and a compass. (a). State the polarity of the ends X and Y. The magnet is then rotated through 180 degrees. Draw the direction of the compass needle when the magnet is at (b) 45°, (c) 90° and (d) 180°.

Figure H.1.2.4

N

S

X Y

X

Y

Y X

(a) (b)

(d)

(c)


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4. The following bar magnets are brought together. In each case, state whether the magnets are attracted or repelled from each other.

Challenge Question 5. For the magnets in question 4, sketch the field between the magnets, clearly labeling regions of uniform field, regions of high field strength, and regions of low field strength.

N S S N N S S N

S N S N

(a) (b)

(c)


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H.1.3. The Magnetic Field of Current Carrying Wires When a charged particle such as an electron moves through space it creates a magnetic field. The field lines form concentric loops centered about the particles path through space, as shown by Figure H.1.3.1.(a). Notice that the field lines have a direction. Since a current in a wire is a flow of charge, a current carrying wire also produces a magnetic field, that form closed loops centered about the wire. To determine the direction of the magnetic field associated with a current carrying wire;

This rule may also be used for the motion of charged particles as long as you remember that a negatively charged particle moves in the opposite direction to the current. Worked example: An electron moves horizontally from right to left in the plane of the page. Sketch the electron and mark the direction of the magnetic field created. Answer. The electron moves from right to left and therefore the current is from left to right (conventional current is in the opposite direction to electron flow). Therefore with the right thumb pointing in the direction of the current, the magnetic field loops are into (×) and out of (·) the page as shown;

Place the right thumb in the direction of the

current, fingers wrap around in the direction of the magnetic field

e v

·

×

·

×

·

×

·

×

·

×

·

×

B

B

e

I

I

B

Figure H.1.3.1.

(a)

(b)


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Just from inspection of the thumb rule, we see that if the current in a wire reverses direction, so does the magnetic field. Thus a D.C current creates a constant field whereas an alternating current creates a time varying field that switches direction with the current. As well as being dependent upon the current, the magnetic field strength B (sometimes called magnetic flux density) is also proportional to the distance r from the wire. The Biot-Savart Law relates the field strength B at a distance r from a wire carrying a current I: The Biot-Savart Law may be used to calculate the magnetic field strength surrounding long straight wires. The permeability of free space µ0 is a fundamental physical constant related to the speed of light c and the permittivity of free space ε0. The unit of the magnetic field strength is the Newton meter per Ampere (Nm/A). This unit is called the Tesla T, after the Serbian physicist Nikola Tesla. Worked Example A long straight wire carries a D.C current of 8A. Calculate the magnetic field strength 20cm from the wire. Answer The distance r from the wire is 0.2m and the current I = 8A. Using the Boit-Savart Law;

𝐵𝐵 =𝜇𝜇0𝐼𝐼2𝜋𝜋𝜋𝜋

=4𝜋𝜋 × 10−7 × 8𝐴𝐴

2 × 𝜋𝜋 × 0.2𝑚𝑚= 1 × 10−6𝑇𝑇

The magnitude of the magnetic field strength B increases with

increasing current


where B = magnetic field strength I = current in the wire µ0 = permeability of free space = 4π×10-7 N/A2

r = distance from the wire (in meters)


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Exercise H.1.3 1. Consider the diagram of the magnetic field surrounding the path traced by a charged particle moving at a velocity v from left to right. Recall that (·) signifies a direction out of the page and (×) a direction into the page, thus the field lines form closed loops. What is the sign of the charged particle? 2. A student pokes a small hole in the center of a square piece of card, through which he passes a current carrying wire. The experimental set up is shown as viewed from above. The student sprinkles iron filings onto the square of card. Sketch the pattern in the filings observed. The student then increases the current by a factor of two. Describe (pictorially if you prefer) the change in the observed pattern of filings. 3. The student in question 2 could have equally used a compass rather than filings to map out the magnetic field lines of the wire. Add the compass needle to compass positioned in the following positions. Mark the compass needle as a single headed arrow with the head of the arrow in the direction of the needles North seeking pole. What would happen to the compass needles if the direction of the current were to be reversed? 4. State the Biot-Savart Law, and use it to calculate the magnetic field strength 5cm from a wire carrying a current of 13A. Challenge Question 5. A magnetic field surrounding a wire is found to have a field strength B = 10µT at a distance of 0.2m from the wire. Calculate the current in the wire.

v ·

×

·

×

·

×

·

×

·

×

·

×

B

Card

× I

× I


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H.1.4. Electromagnets In the previous section we learnt that current carrying wires produce magnetic fields, and that the magnetic field strength B increases with increasing current. To increase B, we could increase the current in the wire by increasing the voltage, however there is an alternative method that allows B to be increased without increasing voltage. Consider the grey region of Figure H.1.4.1 that represents a small region of space through which a current carrying wire passes. The current through the wire is I, and the field strength at point P, a distance r from the wire is given by the Biot-Savart Law;


If we place a single loop in the wire, the wire will pass through the grey region of space twice, and the current in that region will be 2I. A third loop increases the current to 3I, and n loops increases the current by nI. Thus the field at point P has increased to

𝐵𝐵 =𝜇𝜇0𝑛𝑛𝐼𝐼2𝜋𝜋𝜋𝜋

where n is the number of loops in the wire. The magnetic field strength has been increased without the need for a larger battery. Current loops increase the magnetic field strength in the region of space surrounding the loops and are the basis of the electromagnet. A simple electromagnet consists of an insulated current carrying wire wrapped around an iron core such as a nail, as shown by Figure H.1.4.2. (a). The iron core is a soft magnetic material which is not magnetic (or only slightly magnetic) on its own. Figure H.1.4.2. (b) shows a cross section through a small portion of the nail – wire combination, with the wire on one side of the nail coming out of the page and on the other side of the nail into the page. As the current flows though the wire, magnetic field loops are set up around the wire with a direction dictated by the right hand thumb rule. The field from each segment of wire on either side of the core add together in the region of the core since the field is in the same direction. Thus the combined effect from the fields surrounding the wire form a field pattern similar to that of a bar magnet, the strength of which is greatly increased within the coil of wire (a current carrying wire coil with magnetic field equivalent to a bar magnet is called a solenoid).

r

I

r

2I

r

3I

P

P

P

Current Carrying

Wire

Wire Loop

2 Loops

Figure H.1.4.1


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The current induced magnetic field aligns the magnetic moments of the iron core, strongly magnetising it. This adds to the magnetic field strength of the arrangement. Electromagnets have the advantage over permanent magnets that their magnetic effect may be turned off and on by turning the current off and on. Further, reversing the direction of current through the wire changes the direction of the magnetic field lines and reverses the poles of the electromagnet (check this for yourself with the right hand thumb rule). Thus an alternating current will create an electromagnet with poles that switch continuously with a frequency of the alternating current. For electromagnets;

Because of the electromagnets versatility over permanent magnets, they have many applications, a few of the more obvious applications include;

×

×

×

(a) (b)

(c) Figure H.1.4.2.

• Increasing current increases the magnetic field strength • Increasing the number of turns of the wire coil increases magnetic field

strength • Adding a soft magnetic core such as Iron increases the field strength • Magnetic effect may be turned on and off by switching on/off the current • Reversing the current reverses the magnetic poles


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The Scrapyard Crane Powerful electromagnets attached to cranes are used in scrapyards to lift old cars and other heavy metals. The steel in the car frame is attracted to the electromagnet when a current flows (Figure H.1.4.3), allowing the crane to lift the car. When in position, the current is switched off, releasing the car and dropping it into the desired position. Thus the scrapyard crane makes use of the switch ability of the electromagnet. The Circuit Breaker A circuit breaker, as shown in Figure H.1.4.4, breaks a circuit and stops current flow when the current becomes to high, in a similar way to a fuse. In normal operation the switch is held closed by a spring, and the magnetic field of the electromagnet in proximity to the switch is not strong enough to overcome the spring. When too much current flows through the circuit the magnetic field strength of the electromagnet becomes strong enough to overcome the spring, opening the switch and shutting off the current, protecting components in the circuit. The switch remains open and must be closed manually. The Electric Bell When the switch of an electric bell is closed, current flows through the electromagnet as shown in Figure H.1.4.5. The magnetic field of the electromagnet attracts the arm of the striker, simultaneously ringing the bell, and breaking the electrical contacts. This stops current flow around the circuit and through the electromagnet, which releases the striker arm. The striker arm returns to the starting position due to the restoring force of the spring, remaking the contacts. Current can flow one again, and the process repeats until the switch is opened.

Current On

Current Off Figure H.1.4.3.

To Battery

Closed

Open

Electromagnet

Figure H.1.4.4

Cell

I I

N S

Contacts

Striker

Switch Spring

Bell

Figure H.1.4.5.


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Exercise H.1.4 1. A straight wire carries a current of 5A. The wire is then wrapped around an insulating cylinder to form loops. Calculate the magnetic field strength at a point 2cm from the wire when there are; (a) no loops (b) 3 loops (c) 10 loops 2. Describe how a rudimentary electromagnet could be constructed in the classroom. Give three ways in which the strength of the electromagnet could be increased. 3. Explain how a circuit breaker uses an electromagnet to protect components in a circuit from excess current. 4. State how the iron core of an electromagnet increases magnetic field strength Challenge Question 5. Consider the electromagnets below and sketch the field lines, carefully identifying the north and south poles and the direction of the field using the right hand thumb rule.

I I I I

strand h. electromagnetism unit 1. magnets and magnetic fields

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