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Magnetic Field
PH 203
Professor Lee Carkner
Lecture 15
HRW 7 Ed., P 27.20
 Junction rule (at point d)
 i1+i3=i2
 Left loop:

 Right loop:

 Solve loop rule in terms of
common variable, i3
 i1 = (e1+i3R3) / R1
 i2 = (-e2-i3R3) / R2
e1 = 4 V
e2 = 1 V
 Put in numbers
R1 = 10 W

 i2 = -0.1 – 0.5i3
R2 = 10 W
R3 = 5 W
HRW 7 Ed., P 27.20
Put in loop rule
i1+i3=i2
0.4 + 0.5i3 + i3 = -0.1 – 0.5i3
2i3 = -0.5 A

i3 is drawn backwards
i1 = 0.275 A

These are drawn right
Vd –Vc = i2R2 = (0.025)(10)
= +0.25 V
e1 = 4 V
e2 = 1 V
R1 = 10 W
R2 = 10 W
R3 = 5 W
HRW 7 Ed., P 27.26
Power input to circuit is iDV
=
Power dissipated by each
resistor is i2R

Voltage across A and B
must equal voltage of 2 W
and 6 W resistors

i1 = [78 – (6)(6)]/2= 21 A
Junction rule
i1 = i2 + i
i2 = 21 – 6 = 15 A
i2
i1
i=6A
VA-VB =78 V
HRW 7 Ed., P 27.26
Power input to circuit:
Power dissipated by all
resistors (i2R each):

Since the resistors are
using 1998 W and the
applied voltage only
supplies 1638 W, the box
must be providing:
1998 – 1638 = 360 W
i2
i1
i=6A
VA-VB =78 V
Electricity and Magnetism
Magnets exert a force on two types of objects:


Both of these forces are due to the same fact:
Magnetic fields produce a force on moving
charges

Moving charges produce a magnetic field
Both electricity and magnetism are related to
charge
Vectors
A magnet produces a magnetic field (B)

The moving particle has a velocity (v)
All three quantities are vectors

What is the relationship between them?
i.e., if the B field points one way and the charge
is moving another way, what is the direction of
the force?
Right Hand Rule

v
B
F
If v is your
straight fingers,
and you curl
your fingers in
the direction of
B, F is your
thumb
Vector Conventions
The force on a negative particle is
opposite that of a positive one

Vectors going into the page are
represented with a cross (X), vectors
going out of a page are represented with a
dot ()
Magnetic Force Magnitude
The magnitude of the magnetic force
depends on 4 things:

The magnitude of the charge (q)

The angle between the v and B vectors (f)
The force can be written as:
F = qvB sin f
Charged Particle in Field
B
v
f
q
Magnetic Field
We can use the expression for the force to
write an expression for the magnetic field:
B = F/qv sin f

We will often use a smaller unit, the gauss
(G)

Typical bar magnet ~
Earth’s magnetic field ~
Crossed Fields

Electric force: in direction of field

If the E and B field are at right angles to
each other, the forces will be in opposite
directions
Velocity Selector
How could we get the forces to cancel out?
If we “tune” B until the particle is not deflected,
we can find the velocity
Next Time
Read 28.6-28-10
Problems: Ch 28, P: 9, 15, 16, 32, 46
A resistor R and capacitor C are connected to a
battery. If the resistor is replaced with a
resistor of 2R, what happens to the time
needed to charge the capacitor?
A)
B)
C)
D)
E)
It increases
It decreases
It depends on C
It stays the same
None of the above
Over which time range does the charge
on a capacitor increase the least (t=0
is uncharged)
A)
B)
C)
D)
E)
0 to 1t
1t to 2t
2t to 3t
3t to 4t
4t to 5t
Consider a simple circuit consisting of a battery and
resistor. What will happen to the current if a
voltmeter is used to measure the voltage through
the resistor? What will happen to the current if a
ammeter is used to measure the current through
the resistor?
A)
B)
C)
D)
E)
increase, increase
increase, decrease
decrease, decrease
decrease, increase
You can’t tell without knowing the voltage of the
battery