Electromagnetism- How Does A Compass Work PDF

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Electromagnetism: How Does A Compass Work? Magnets

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When there is no magnet near a block of iron, the domains inside the iron act as mini magnets and are all randomly aligned

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Domains inside the iron try to align with the magnetic field of a magnet To increase the time for the domains to return back to being randomly aligned: ○ Apply a very strong magnetic field ○ Heat in the presence of a magnetic field ○ Hitting it with a hammer in the presence of a magnetic field ○ Stroking a magnet for a longer time Maxwell showed that electricity and magnetism were part of the same combined theory of electromagnetism

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FCoulomb =k

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q1 q2 r2

where FCoulomb = force (N)

k = Coulomb’s constant (8.99 x 109 Nm2C-2) q1 = charge 1 (C) q2 = charge 2 (C) r = radius (m) Two like charges repel each other Two unlike charges attract each other

Magnetic fields are vectors ○ Unit: Tesla ○ Symbol: B

The Earth’s Magnetic Field

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Outer core consists of iron ○ Conducts electricity ○ Any current has a magnetic field

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Inside of the earth is acting like a bar magnet with a south pole at the north pole of the earth as unlike poles attract

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B Earth ≈ 25−65 μ T

One magnetic pole is in Canada and Antarctica Paleomagnetism allows us to trace where the magnetic north and south pole were in the past ○ Geologist look at the alignment of ferromagnetic crystals in rocks ○ When a volcano erupts producing igneous rocks, the crystals are able to move (the rock is runny) and align themselves with the earth’s magnetic field ● Earth’s magnetic field keeps us safe from solar radiation Solar Wind: stream of charged particles from the Sun

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Some particles intersect with Earth i.e. radiation Earth’s magnetic field causes the particles to travel in a helical path ○ Doesn’t hit the earth directly ○ Usually hit at the south and north magnetic pole ○ Able to observe the ionised particles hitting the earth’s atmosphere i.e. Northern and Southern lights ■ Causes nitrogen and oxygen atoms to ionise but then regain their electrons and unionise, releasing a photon

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Earth’s magnetic field are important for the atmosphere ○ Protect the ozone layer Helical path causes a concentration of the particles ○ Van Allen Belts

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Some animals can sense the earth’s magnetic field ○ Bacteria with ferromagnetic materials in them align to the earth’s magnetic field ○ Birds can sense magnetic fields ■ Used when migrating for navigation

Force On A Charged Particle In A Magnetic Field ● ●

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Electromagnetism is responsible for converting energy generated by nuclear power into electricity 1820, Hans Christian Earthstead observed that if a strong current flowing through a wire and moved a compass needle through it, the wire deflected the needle ○ Indicated a magnetic field 1864, James Clerk Maxwell came up with the theory of electromagnetism

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Linked electricity, magnetism and light

F=Bqvsin θ

where F = force (N) B = magnetic field strength (Tesla) q = charge (C) v = speed (ms-1) θ = angle between magnetic field and velocity of charged particle (o)

Right Hand Rule

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For negative particles, the force is protruding from the back of the hand

Example: A proton is shot with a velocity of 2.00 x 105 ms-1 into a magnetic field, with a

magnetic fields strength of 5.00 mT. Assume that the velocity and the magnetic field are at right angles to each other. a) Draw a diagram showing this situation

b) Calculate the force felt by the proton in your diagram

F=Bqvsin θ=5.00 ×10−3 × 1.602×10−19 × 2.00× 105 × sin 900 = 1.602 x 10-16 N into the screen c) What is the acceleration of the proton in this case? F = ma →

F 1.602× 10−16 =9.58 ×10 10 m s−2 into the screen a= = m 1.673 × 10−27

d) If the velocity of the proton makes an angle of 30.0o with the magnetic field what is the magnitude of the force felt by the proton?

F=Bqvsin θ=¿

1.602 × 10−19 × sin 30=8.01 ×10−17 N

A helium nucleus with a mass of 6.64 x 10-27 kg and a charge of 3.204 x 10-19 C enters a region with a magnetic field strength of 10.0T. The arrangement is shown in the diagram. The speed of the helium nucleus is 3.00 x 106 ms-1

a) What force does the helium nucleus initially experience? −19

F=Bqvsin θ=10.0 ×3.204 × 10

6

× 3.00 ×10 ×sin 90=9.61 ×10

−12

N to the left

b) Explain why the helium nucleus experiences circular motion The force and acceleration is always at right angles to the velocity of the particle. When acceleration and velocity are always perpendicular and constant, a particle undergoes circular motion c) Calculate the radius of the circular path followed by the helium nucleus −27

2

Fc =

mv =Bqvsinθ → r

r=

6

2 6.64 ×10 × (13.00 × 10 )❑ mv = −12 Bqvsin θ 9.612 ×10

= 6.22 x 10-3 m

2

Force On A Current Carrying Wire F=BIlsin θ

where F = force (N) B = magnetic field strength (T) I = current (A) L = length of wire in field(m) θ = angle (o)

Right Hand Rule

Example: A conducting bar with a mass of 5.00 g is hung in a 1.20T magnetic field directed into the screen. What current needs to flow along the wire in order for the bar to just lift above the supports. Assume the supports are 10.0cm apart

Current must flow from left to right

mg=BIlsin θ right

→

I=

−3 mg = 5.00 ×10 × 9.80 =0.408 A BIlsin θ 1.20× 0.100 ×sin 90

from left to

Magnetic Field Around A Wire

Right Hand Screw Rule

B=

μ0 I 2π r

where B = magnetic field strength (T)

μ0 = permeability of free space (4π x 10-7 TmA-1) I = current (A) r = distance from wire in field (m) Example: A wire carries a current of 2.50 A

a) Calculate the magnetic field strength at point P located 5.00 cm from the wire

B=

μ0 I 4 π ×10−7 × 2.5 = =1.00 × 10−5 T 2π r 2 π × 0.0500

out of the screen

b) Sketch a graph showing how B varies with distance from the wire

Force Between Two Wires Derivation

F2 =B1 Ilsinθ μ0 I μ I out of screen B 1= 0 1 = 2π r 2 π d F2 =

μ0 I 1 μ I I l × I 2 lsin 90= 0 1 2 towards wire 1 2π d 2πd

The force will be repulsive if the currents travel in opposite directions

F❑ =

μ0 I 1 I 2 l 2πd

where F = force on wire 2 (N)

μ0 = permeability of free space (4π x 10-7 TmA-1) I1 = current in wire 1 (A) I2 = current in wire 2 (A) L = length of wire (m) d = distance between wires (m)

Example: A current carrying loop (I2 = 7.5 ) is set up next to a current carrying wire (I1 = 10 A) as shown in the diagram. Ignore any external forces such as gravity

a) Calculate the net force on side 1 F1 =

μ 0 I 1 I 2 l 4 π ×10−7 × 10× 7.5× 0.20 =3.0 ×10−5 N towards wire 1 = 2 π ×0.10 2π d

b) Calculate the force on side 3 F3 =

μ0 I 1 I 2 l =¿ 2π d

4 π ×10−7 × 10 × 7.5 × 0.20 =1.5 ×10−5 N away ¿ wire 1 2 π × 0.20

c) Comment on the relationship between forces felt on sides 2 and 4 Sides 2 and 4 both feel a force as they are current carrying wires in a magnetic field generated by wire 1. Side 2 feels an upwards force while side 4 experiences a downwards force. These forces have the same magnitude but opposite direction d) Calculate the net force on the loop Fnet = F1 + F3 = 3.0 ×10−5 - 1.5 ×10−5 =

Electromagnets Solenoid

−5

1.5 ×10

towards wire 1

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Iron can increase the strength of magnetic fields

Applications ● Junk car yards ● Electromagnetic braking...