F. Electricity and Magnetism · Electricity and MagnetismOersted's Principle, the Right-Hand Rules and Electromagnets
F2.5 F3.1 F3.2 F3.3 F3.4 F3.5About 75 minutes
Learning goals- I can state Oersted's principle and describe the field around a straight conductor and a solenoid.
- I can use the first and second right-hand rules (conventional current) and the matching left-hand rules (electron flow).
- I can read and draw dot and cross notation for directions into and out of the page.
- I can explain the factors that affect the strength of an electromagnet and describe some uses.
Words to know
Oersted's principle
Charge moving through a conductor produces a magnetic field around the conductor.
right-hand rule #1 (RHR #1)
For a straight conductor: grasp the wire with your right hand with your thumb along the conventional current; your curled fingers show the direction of the circular magnetic field.
right-hand rule #2 (RHR #2)
For a coil or solenoid: curl the fingers of your right hand in the direction of the conventional current in the loops; your thumb points to the N end of the coil.
left-hand rules
The same rules done with the left hand when you use electron flow instead of conventional current.
solenoid
A long coil of wire. When it carries a current, its field is like that of a bar magnet.
electromagnet
A solenoid wrapped around a soft-iron core. It is a magnet only while current flows.
• and ×
Symbols for direction perpendicular to the page: • means out of the page (an arrow's point coming at you); × means into the page (an arrow's tail feathers going away).
The compass that twitched
In 1820, the Danish physicist Hans Christian Ørsted noticed that a compass needle swung when he switched on a current in a nearby wire. Until then, electricity and magnetism were thought to be separate subjects. Ørsted had found the link: a current makes a magnetic field.
Every electric motor, speaker, doorbell, MRI scanner and hard-drive head depends on that link. In this lesson you will learn to predict the shape and direction of the field around a wire and a coil.
Oersted's principle
Charge moving through a conductor produces a magnetic field around the conductor.
For a long straight wire, the field lines are circles centred on the wire, in planes perpendicular to it. The field is:
- stronger when the current is larger (B is proportional to I), and
- weaker farther from the wire (for a long straight wire, B is inversely proportional to the distance r, so doubling the distance halves the field).
If the current reverses, the field reverses.
Dots and crosses
Directions into and out of the page are drawn with symbols. Imagine an arrow. • is the point of the arrow coming straight at you: out of the page. × is the tail feathers of an arrow flying away from you: into the page.
Right-hand rule #1: straight conductor
Pretend to grab the wire with your right hand, with your thumb pointing in the direction of the conventional current. Your fingers curl in the direction of the magnetic field.
If you use electron flow instead, use your left hand with the thumb along the electron flow. Since electrons move opposite to conventional current, and the left hand curls the opposite way, you get the same field direction. Choose one convention and stay consistent. This is the link between conventional current, electron flow and the hand rules.
Loops and solenoids
Bend the wire into a loop. All around the loop, the field inside points the same way, so the fields add up and the field in the middle is concentrated. Stack many loops into a solenoid and the field inside becomes strong and nearly uniform, while the field outside looks just like a bar magnet's field. One end acts as an N pole and the other as an S pole.
Right-hand rule #2: coil or solenoid
Wrap the fingers of your right hand around the coil in the direction of the conventional current in the loops. Your thumb points to the N pole of the coil (the direction of the field inside the coil). With electron flow, do the same with your left hand.
A handy check: look at one end of the coil. If the conventional current goes counterclockwise as you look at it, that end is N; if clockwise, it is S.
Electromagnets
Put a soft-iron core inside a solenoid and the field becomes hundreds of times stronger, because the coil's field aligns the domains in the iron, and the iron's field adds to the coil's. Switch off the current and the soft iron loses most of its magnetism. You can increase an electromagnet's strength by:
- increasing the current,
- increasing the number of turns (more turns per unit length), and
- using a better core (soft iron is much better than air or aluminium).
There is a limit: once nearly all the domains in the core are lined up, the core is saturated and more current helps much less.
Electromagnets are everywhere: scrapyard lifting magnets, magnetic door locks, relays (a small current switches a large one, as in a car's starter circuit), electric bells, speakers, MRI scanners and maglev trains. Unlike a permanent magnet, an electromagnet can be switched on and off, its strength can be adjusted, and its poles can be reversed by reversing the current.
Worked exampleExample 1: Field around a straight wire
A long wire runs up the page with conventional current upward. What is the direction of the magnetic field (a) at a point 2 cm to the right of the wire, (b) at a point 2 cm to the left? (c) How would the answers change if the current reversed?
- Point your right thumb up the page, along the current. Your fingers curl around the wire.
- (a) On the right side, your fingers go into the page (×).
- (b) On the left side, they come out of the page (•).
- (c) Reversing the current reverses the field: right side out of the page, left side into the page.
(a) into the page, (b) out of the page, (c) both reverse.
Worked exampleExample 2: Finding the N end of a solenoid
A horizontal solenoid is connected to a battery. Looking at its left end, you see the conventional current going clockwise around the loops. Which end is the N pole? What happens if the battery is turned around?
- Curl your right fingers clockwise as you look at the left end. Your thumb points away from you, into the coil, toward the right.
- The thumb shows the field inside and the N pole, so the right end is N and the left end is S.
- Check: from the left end the current looks clockwise, so that end is S ✓.
- Turning the battery around reverses the current, so the poles swap: left N, right S.
The right end is N; reversing the battery swaps the poles.
Worked exampleExample 3: The same answer with electron flow
Electrons flow to the right along a horizontal wire. Use a left-hand rule to find the direction of the field just above the wire. Then check with conventional current and RHR #1.
- Left hand: thumb to the right (electron flow). Your left fingers curl so that above the wire they point into the page.
- Check: conventional current is to the left. Right thumb to the left: above the wire the right fingers point into the page. ✓
- Both conventions give the same field, as they must, because the physics does not change.
Into the page above the wire.
Just for funWhy did the compass needle start following the wire around?
It had developed a current interest.
Hands-on activityMake an electromagnet and repeat Ørsted's discovery
You need: one large iron nail (about 8 cm), about 1 m of thin insulated wire (bell wire or wire from an old kit, with the insulation scraped off only at the two ends), one D or AA alkaline battery, tape, a compass (or phone compass), and paper clips. Grown-up note: a coil connected to a battery is close to a short circuit, so the wire and battery get hot quickly. Connect only for a few seconds at a time, never use rechargeable lithium batteries or anything bigger than a single D or AA cell, and let things cool between trials.
Part 1, Ørsted: lay a straight part of the wire on top of the compass, lined up with the needle (north–south). Touch the ends to the battery for 2 seconds. Watch the needle. Reverse the battery and repeat.
Part 2, electromagnet: wind 20 turns of wire tightly around the nail, all in the same direction, and tape them in place. Connect briefly and count how many paper clips the nail can lift. Then rewind to 40 turns and repeat. Bring the compass near each end to find the N pole, and check your answer with RHR #2.
What to look for: in Part 1 the needle swings sideways, and swings the other way when you reverse the current (Oersted's principle). In Part 2, more turns usually lift more paper clips, and the N end found with the compass matches RHR #2. When you disconnect, the nail drops most of the clips (soft iron loses its magnetism).
Your turn
1State Oersted's principle.
Charge moving through a conductor produces a magnetic field around the conductor.
2A wire runs up the page with conventional current upward. Which way does the field point just to the left of the wire?
By RHR #1, out of the page (•).
3Conventional current flows into the page (×). Is the field around the wire clockwise or counterclockwise as you see it?
Clockwise. (Point your right thumb into the page; your fingers curl clockwise.)
4What do the symbols • and × mean?
• means out of the page; × means into the page.
5Looking at one end of a solenoid, you see the conventional current going counterclockwise. Is that end N or S?
N. Curl your right fingers counterclockwise as you look: your thumb points toward you, out of that end.
6List three ways to make an electromagnet stronger.
Increase the current, increase the number of turns (per unit length), and use a soft-iron core (a better core material).
7Electrons flow to the right along a horizontal wire. What is the direction of the field just below the wire?
Conventional current is to the left. Right thumb left: below the wire the fingers come out of the page. (Left-hand rule with electrons gives the same answer.)
More practice: warm-up
1Who discovered that an electric current makes a magnetic field, and in what year?
Hans Christian Ørsted, in 1820.
2In RHR #1, what does the thumb represent and what do the fingers represent?
Thumb: conventional current. Fingers: the direction of the magnetic field circling the wire.
3Which hand do you use for the rules if you work with electron flow?
4What shape are the field lines around a long straight wire?
Circles centred on the wire.
5True or false: the field around a wire is stronger closer to the wire.
True. It gets weaker with distance.
More practice: on your own
1A vertical wire carries conventional current straight up out of the ground. Viewed from above, compasses sit just north, east, south and west of it. Which way does each compass point? (Ignore Earth's field.)
Viewed from above the current comes toward you, so the field is counterclockwise. East of the wire: north. North of the wire: west. West of the wire: south. South of the wire: east.
2The current in a long wire is doubled and you move three times farther away. How does the field compare with before?
B is proportional to I ÷ r: (2) ÷ (3) = 2/3 of the original field.
3Why does a solenoid's field look like a bar magnet's?
Inside the coil, the fields of all the loops point the same way and add up, making a strong field along the axis. The lines leave one end (N), loop around outside and enter the other end (S), just like the field of a bar magnet.
4Give three advantages of an electromagnet over a permanent magnet.
It can be switched on and off, its strength can be adjusted (by changing the current), and its poles can be reversed (by reversing the current).
5A solenoid's N pole is at its left end. Looking at the left end, which way does the conventional current go around the loops?
Counterclockwise. An end where the current appears counterclockwise is the N end (your right thumb points toward you).
Challenge
1Two long parallel wires are 10 cm apart and carry equal currents. (a) If both currents come out of the page, what is the field at the midpoint? (b) What if the currents are in opposite directions?
(a) At the midpoint each wire's field is the same size. With both currents out of the page, the counterclockwise fields point in opposite directions there (one up the page, one down), so they cancel: B = 0. (b) With opposite currents, the two fields point the same way at the midpoint, so the field is twice that of one wire.
2Explain how a relay lets a small current in a car's ignition switch control the very large current to the starter motor.
Turning the key sends a small current through the relay's coil, making it an electromagnet. It attracts a soft-iron armature that closes a separate set of heavy contacts, completing the high-current starter circuit. When the key is released, the coil switches off, a spring pulls the armature back and the big circuit opens. The ignition switch and thin wires never carry the large current.
3A student's electromagnet lifts 6, 12 and 18 paper clips with 50, 100 and 150 turns at 1.0 A. She predicts that with 100 turns at 4.0 A it will lift 48 clips, but it lifts only about 30. Explain the pattern and the surprise.
At first, strength is roughly proportional to the number of turns (and to current): 6 clips per 50 turns. Raising the current should multiply the strength, but the iron core saturates: once nearly all its domains are aligned, extra current adds much less field. (The coil also heats up, which raises its resistance and can lower the current.)
Quiz
1. What is Oersted's principle?
2. Conventional current flows out of the page (•). What is the direction of the magnetic field around the wire, as seen on the page?
3. In RHR #2 for a solenoid, what does the thumb point to?
4. A student uses electron flow. Which rule should she use to get correct field directions?
5. Which change would NOT make an electromagnet stronger?
6. A wire runs left to right across the page with conventional current to the right. What is the field direction just above the wire?
Big idea: Oersted's principle (F3.4) links electricity and magnetism. This lesson covers the field around a straight conductor and a solenoid (F2.5), the right-hand rules (F3.2), how conventional current and electron flow relate to right- and left-hand rules (F3.3), and electromagnets (F3.1, F3.5).
How to help: Ask your teen to show you the hand rules with their actual hand; physics students really do this on tests. The electromagnet activity is classic, but please supervise: the wire and battery heat up quickly, so connect for only a few seconds at a time.
Common difficulties:
- Using the right hand with electron flow (or the left with conventional current). Agree on one convention and label every arrow.
- Mixing up RHR #1 (thumb = current) and RHR #2 (fingers = current, thumb = N).
- Reading • and × the wrong way round. Remember the arrow: point coming at you, feathers going away.
- Thinking the field is the same everywhere around a wire; it gets weaker with distance.