Electromagnetism - The Burns Home Page

03/12/2010 

Electromagnetism Canada’s Triumph Accelerator 

Putting it All Together 

Hydrogen Minus 

Electromagnetism 

Initial Acceleration 

Electrostatic 

Circular Motion 

Magnetic Steering 

Filtering 

Electromagnetism Review 


Magnetic Flux 

Magnetic Flux 

Flux can be described as the total number of lines passing though an area, loop or coil. 

We can describe the Density (or 

amount) of a Magnetic Field with the 

concept of Magnetic Flux. 

Flux can be described as the total 

number of lines passing though an 

area, loop or coil. 

It is a quantity of convenience used in 

Faraday’s Law. 

Magnetic Flux 

B BAcos 

 

Magnetic Field 

(Tesla) 

Angle between field 

and normal line (B) 

on the Surface Area 

Area of Surface 

(m 2 ) 

This can be 

described by 

the equation 

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03/12/2010 


B BAcos 

 

Magnetic Flux Observations 


Magnetic Flux Units 

The Stronger the Magnetic Field (B), 

the greater the Flux (). 

Since 

B = BAcos(θ) 

Flux has the 

units of B x A 

The larger the Area (A), the greater 

the Flux (). 

This is also called 

a Weber (Wb) 

This is 

(Tesla)(Metre 2 ) 

If the Magnetic Field (B) is 

perpendicular to the area, then the 

Flux () will be at a maximum. 


Magnetic Flux Units 


Magnetic Flux by Larger Area 

When the field is perpendicular 

to the plane of the loop 

θ = 0 and Φ B = Φ B, max = BA 

When the field is parallel to the 

plane of the loop. 

θ = 90° and Φ B = 0 

The flux can be negative, for 

example if θ = 180° 

When the field is at an angle θ to 

the field B, Φ B is less than 

max. 

You can increase the 

magnetic Flux by 

increasing the 

Surface Area 

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Magnetic Flux by Strengthening the Field 


Magnetic Flux Practice Question 

B BAcos 

 

You have a hula loop of radius 0.5m that is immersed 

in the Earth’s magnetic field (5x10 -5 T). The hula loop 

is oriented in such a way that the normal is tilted at an 

angle of 20 0 away from the Earth’s North pole. What is 

the flux through the hoop? 

B BAcos 

 

B 

 

 

B r 2 cos 

You can increase the 

magnetic Flux by 

Strengthening the Field. 

.5 20 

 

 

B 5 10 T 0 m cos 

5 

3.710 

Wb 

B 

5 2 


Faraday’s Law 



Induction 

Law of Induction 

Faraday’s Law describes the 

relationship between Electric Current 

and Magnetism. 

An Electric Current can induce a 

Magnetic Field, and a Magnetic Field 

can induce a Electric Current. 

Induced Voltage, V. 

A voltage is generated a Magnetic 

Force has been traditionally called 

an Electromotive Force or emf. 

The number of coils 

of wire 

 

N 

t 

Change in Magnetic 

Flux, Wb 

Change in time, s 

Just as Electricity needs to be moving 

to create a Magnetic field B, The 

Magnetic field B needs to be moving 

to create an Electric Current . 

•The greater the change in Magnetic Flux in a wire loop, the 

greater the Induced Current. 

•Less time corresponds to a greater Induced Current. 

•Adding more loops corresponds to a greater Induced Current. 

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03/12/2010 


 

N 

t 

Faraday’s Law Practice Question 


B Direction 

Lenz’s Law 

You have a coil of wire with 30 loops, each of which has 

an area of 2.0 x 10 -3 m 2 . The Magnetic Field B is 

perpendicular to the surface. At time t=0 s, the Field B is 

measured at 1.0 T. At time, t=.2 s, the Field B is measured 

at 1.1 T. What is the average emf inside the coils. 

Lenz’s Law describes the direction of 

the Electric Current produced by a 

changing Magnetic Field. 

 

N 

t 

BAcos 

 

N 

t 

 

0.03V 

B BAcos 

 

1.1 1.0 2.0 10 3 2 

T T m cos 0 

 

30 

0.2s 

0.0s 

The Thumb points in the direction of 

the Current. The fingers curl in the 

direction of the Magnetic Field. 


Lenz’s Law 


Lenz’s Law 

B Direction 

Change in Flux 

An influenced emf gives rise to a 

Electric Current whose Magnetic Field 

opposes the original change in Flux. 

The Right Hand Rule can aid us in 

these situations. 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

Notice how the area is lessened when the loop is stretched. 

Since the Flux is reduced, the Electric Current flows in the 

direction that would produce the B field. This direction tries 

to help maintain the original Flux. 

The induced current attempts to maintain the status quo. 

4

N 

S 

03/12/2010 


Lenz’s Law 


Lenz’s Law 

Hoop Entering B Field 

Hoop Inside B Field 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

When the loop enters a Magnetic 

Field. An Electric Current is induced 

(counter clockwise) in the loop as to 

oppose the increase in the Flux inside 

the loop. 

When the loop is total immersed 

inside a Magnetic Field there is No 

increase in Flux therefore there is No 

Current flow in the loop. 


Lenz’s Law 


Lenz’s Law 

Hoop Exiting B Field 

Magnet Moving Through Hoop 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

X X X X X X X 

When the loop exits a Magnetic Field. 

An Electric Current is induced 

(clockwise) in the loop as to oppose 

the decrease in the Flux inside the 

loop. 

When a magnet enters the 

loop passes the through current will flow 

clockwise a closed loop, (to oppose the 

increase the current in flux, will make the 

end flow of in the what loop the magnet 

enters directions? act like a North 

Pole) then zero. As the 

magnet exits, the current 

will then flow counter 

clockwise (to oppose the 

decrease in flux, ie look 

like a South Pole). 

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03/12/2010 


Lenz’s Law 


EMF 

Magnet Moving Through Hoop 

EMF induced in a Moving 

Conductor 

When the North end of a 

The magnet current enters will the flow loop clockwise from 

to behind oppose the the screen, increasing which flux. 

direction, if any, will the 

current flow in the wire? 

We have a conducting bar moving across 

a U shaped wire. The magnetic field is 

coming out of the screen. As the bar 

moves across the wire, the amount of Flux 

inside the loop increases. 




EMF 

EMF in a Moving Conductor 

EMF induced in a Moving Conductor 

Induced Electromotive Force or emf. 

Velocity in m/s. 

A 2.0 m rod is moving at 7 m/s perpendicular 

to a 1.2 T magnetic field heading into the 

screen. Determine the induced emf. 

BLv 

Magnetic Field in T. 

Length of moving 

conductor in m. 

X X X X X X X X X X X 





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03/12/2010 


EMF 


Recall 

EMF induced in a Moving Conductor 

Force of Magnetic Field on Current 

BLv 

m 

1.2T 2.0m7 

 

s 

17V 






• Force on 1 moving charge: 

‣ F = q v B sin() 

‣ Out of the page (RHR) 

• Force on many moving charges: 

‣ F = (q/t)(vt)B sin() 

= I L B sin() 

+ 

‣Out of the page! 

+ 

 

v 

+ + + 

v 

L = vt 

B 

I = q/t 

distance 

Torque on Current Loop in B field 

W 

d 

a 

• F 

L 

Force on sections B-C and A-D: F = IBW 

Torque on loop is t = L F sin(f) = ILWB sin(f) 

Torque is 

I 

(length x width = area) 

c 

F 

X 

b 

B 

t = I A B sin(f) 

LW = A 

F 

d 

f 

a 

b 

c 

F 

Understanding: Torque on 

Current Loop 

What is the torque on the loop below? 

1 

2 

3 

t < IAB 

t = IAB 

t > IAB 

t = 0 

x x x x x x x x x x x x x x x x 








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03/12/2010 

Torque on Current Loop 

Understanding: Torque 

Magnitude: 

t = I A B sinf 

F 

f 

B 

B 

B 

Direction: 

Torque tries to line up the normal with B! 

(when normal lines up with B, f=0, so t=0! ) 

Even if the loop is not rectangular, as long as it is flat: 

# of 

loops 

between normal and B 

t = N I A B sinf. 

(area of 

loop) 

F 

I 

(1) 

Compare the torque on loop 1 and 2 which have 

identical area, and current. 

Area points out 

of page for both! 

1) t 1 > t 2 2) t 1 = t 2 3) t 1 < t 2 

t = I A B sinf 

(2) 

f = 90 degrees 

B 

B 

- 

+ 

+ v 

F 

L 

- 

+ 

Motional EMF 

Moving + charge feels force downwards: 

v 

F = q v B sin() 

Velocity 

Moving + charge still feels force downwards: 

Potential Difference F d/q 

EMF = q v B sin() L/q 

= v B L 

Angle between 

v and B 

Understanding 

• Which bar has the 

larger motional emf? a b 

ε = v B L sin() 

is angle between v and B 

Case a: = 0, so ε = 0 

Case b: = 90, so ε = v B L 

v 

“a is parallel, b is perpendicular” 

v 

Velocity 

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03/12/2010 

Motional EMF circuit 

Moving bar acts like battery = vBL 

• Magnitude of current 

I = /R = vBL/R 

• Direction of Current 

Clockwise (+ charges go down thru bar, up thru bulb) 

• Direction of force (F=ILB sin()) on bar due to 

magnetic field 

What changes if B 

points into page? 

To left, slows down 

B 

- 

+ 

V 

Motional EMF circuit 

Moving bar acts like battery = vBL 

• Magnitude of current 

I = /R = vBL/R 

• Direction of Current 

Still to left, slows down 

B 

x x x x x x x x x x x x x x x x x 


V 

+ 


- 



Counter-Clockwise (+ charges go up thru bar, down thru bulb) 

• Direction of force (F=ILB sin()) on bar due to 

magnetic field 

Understanding 

Suppose the magnetic 

field is reversed so that it 

now points OUT of the 

page instead of IN as 

shown in the figure. 

X o X o o X o X o X o v X o X o X o X o o X o X 

X o X o o X o X o X o X o X o X o X o o X o X 


X o X o o X o X o X o X o X o X o X o o X o 

F 

X 

m 


To keep the bar moving at the same speed, the force 

supplied by the hand will have to: 

• Increase 

• Stay the Same F=ILB sin()) 

• Decrease 

B and v still perpendicular (=90), so F=ILB just 

like before! 

Understanding 

Suppose the magnetic 

field is reversed so that 

it now points OUT of the 

page instead of IN as 

shown in the figure. 

X o X o o X o X o X o v X o X o X o X o o X o X 



X o X o o X o X o X o X o X o X o X o o X o 

F 

X 

m 


To keep the bar moving to the right, the hand will 

have to supply a force in the opposite direction. 

• True 

BLv 

BLv 

• False 

I 

R 

Current flows in the opposite direction, so force 

direction from the B field remains the same! 

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03/12/2010 

Applications of Magnetic Force 

Examples of Induced Current 

Any change of current in primary induces a current in secondary. 

Electric currents (in a wire, in a plasma, in a fluid solution, inside an 

atom) produce a disturbance in the surrounding space called the 

magnetic field. This magnetic field produces forces on any other 

macroscopic or microscopic currents. 

Example: MRI: Magnetic field (several Tesla) from superconducting 

solenoid induces a net alignment of the microscopic currents inside 

each and every proton at the center of the Hydrogen atoms in your 

body. 

Induced Current 

Transformers 

A transformer is a device used to change the voltage in a 

circuit. AC currents must be used. 

• The current in the primary polarizes the material of the core. 

• The magnetic field of the primary solenoid is enhanced by the 

magnetic field produced by these atomic currents. 

• This magnetic field remains confined in the iron core, and only fans 

out and loops back at the end of the core. 

• Any change in the current in the primary (opening or closing 

switch) produces a change in the magnetic flux through the 

secondary coil. This induces a current in the secondary. 

75,000 V in the 

power lines 

I Vp 

N 

s 

p 

 

I p Vs 

Ns 

p = primary 

s = secondary 

120 V in your house 

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03/12/2010 

Generator 

A coil of wire turns 

in a magnetic field. 

The flux in the coil 

is constantly 

changing, 

generating an emf 

in the coil. 

Wires: 

Flux area: 

Electric/Magnetic Balance: 

Applets 

Flux: 

Induced Current: 

Moving Bar: 

Generator: 

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