Physics 6B
Magnetic Forces and Fields
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What creates a magnetic field?
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What creates a magnetic field?
Answer: MOVING CHARGES
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What creates a magnetic field?
Answer: MOVING CHARGES
What is affected by a magnetic field?
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What creates a magnetic field?
Answer: MOVING CHARGES
What is affected by a magnetic field?
Answer: MOVING CHARGES
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What creates a magnetic field?
Answer: MOVING CHARGES
What is affected by a magnetic field?
Answer: MOVING CHARGES
We have a formula for magnetic force on a moving charge:

 
Fmag  q  v  B  q  v  B  sin()
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What creates a magnetic field?
Answer: MOVING CHARGES
What is affected by a magnetic field?
Answer: MOVING CHARGES
We have a formula for magnetic force on a moving charge:

 
Fmag  q  v  B  q  v  B  sin()
This is a vector cross-product. We need a right-hand-rule to find the direction of this force.
How to find the direction:
0)Use your RIGHT HAND
1)Fingers start in the direction of the charge’s velocity.
2)Curl fingers toward the direction of the magnetic field.
3)Thumb points in the direction of the magnetic force on the charge.
4)If the charge is negative, flip your hand over.
Important notes: If velocity is aligned with the magnetic field, force is zero.
Magnetic force is always perpendicular to both the velocityPrepared
and the
B-field.
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Zaccone
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A uniform magnetic field is directed into the page.
Find the direction of the magnetic force on charge A, a positive charge.
X
 X
B
X
X
X
X
X
X
X

vA
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
A
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A uniform magnetic field is directed into the page.
Find the direction of the magnetic force on charge A, a positive charge.
X
 X
B
X
X
X
X

vA
X
X
X
Fmag
A
-Fingers start along A’s velocity (up in the picture)
X
X
X
-Fingers bend toward B-field (into the page)
-Thumb sticks out to the left.
X
X
X
X
X
X
X
X
X
X
X
X
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A uniform magnetic field is directed into the page.
Find the direction of the magnetic force on charge B, a positive charge.
X
X
 X
B
X

vB
X
X
X
X
X
X
X
X
B
X
X
X
X
X
X
X
X
X
X
X
X
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A uniform magnetic field is directed into the page.
Find the direction of the magnetic force on charge B, a positive charge.
X
X
 X
B
X
X

vB
X
X
X
X
X
X
X
-Fingers start along B’s velocity (up and to the left
in the picture)
-Fingers bend toward B-field (into the page)
-Thumb sticks out down and to the left.
B
X
X

X
Fmag
X
X
X
X
X
X
X
X
X
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A uniform magnetic field is directed into the page.
Find the direction of the magnetic force on charge C, a negative charge.
X
 X
B
X
X
X
X
X
X
X
X
X
X

vC
C
X
X
X
X
X
X
X
X
X
X
X
X
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A uniform magnetic field is directed into the page.
Find the direction of the magnetic force on charge C, a negative charge.
X
X
 X
B
X
X
X
X
X
X
X
X
X

vC
C
-Fingers start along C’s velocity (to the right in the
picture)
-Fingers bend toward B-field (into the page)
-Thumb sticks out upward.
X
X
X
X

Fmag
X
X
X
X
X
X
X
X
-Force is downward. (negative charges are
pushed in the opposite direction)
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A uniform magnetic field is directed into the page.
Now that we can find the force on a charge, we should be able to predict its trajectory.
Notice that the force is always perpendicular to the velocity. This will yield a circular
path. In other words, the magnetic force is a centripetal force.
X
 X
B
X
X
X
X
Notice that in this diagram, A is a positive
charge, and moves counter-clockwise.

vA
X
X
X
Fmag
A
X
X
X
X
X
X
X

vC
C
X
X
Since B is a negative charge, it moves the
opposite direction - clockwise.
So you can tell the sign of the charge by which
direction it rotates in a magnetic field.
X

Fmag
X
X
X
X
What path would a neutral charge follow?
X
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A uniform magnetic field is directed into the page.
Find the direction of the magnetic force on the wire, with current flowing as shown.
X
 X
B
X
X
X
X
I
X
X
X
Fmag
X
X
X
Pretend that positive charges are flowing in the
direction of the current.
-Fingers start along A’s current (up in the picture)
-Fingers bend toward B-field (into the page)
-Thumb sticks out to the left.
X
X
X
X
X
X
There is a formula for the force
on a wire in a B-field:
X
X
X
X
X
X
Fmag  I  L  B  sin( )
Length of wire
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Mass Spectrometer
Ions are fired into a region of constant magnetic field.
Magnetic force pushes it into a circular path and the impact location
will determine the mass/charge ratio of the ion.
𝐹𝑚𝑎𝑔 = 𝐹𝑐𝑒𝑛𝑡
𝑚𝑣 2
𝑞𝑣𝐵 =
𝑟
𝑚𝑣
𝑟=
𝑞𝐵
Velocity selector
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Application: Torque on a current loop.
The square loop of wire has current I running through it as shown. If a uniform magnetic field
passes through the loop it will rotate due to the magnetic forces on the 4 sides of the loop.
Note that the net force will be zero, but the loop will spin in an attempt to align itself with the
magnetic field (so that the maximum number of field lines pass through the loop).
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How can you create a magnetic field?
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How can you create a magnetic field?
Answer: move some charges (e.g. make current flow in a wire)
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How can you create a magnetic field?
Answer: move some charges (e.g. make current flow in a wire)
Magnetic Field Near a Long Straight Wire:
This formula gives the magnitude of the
magnetic field near a wire. The B-field
takes the shape of concentric rings
centered on the wire.
B
0  I
2  R
0  4  107
T m
A
R = distance from wire
A right-hand-rule will give the orientation:
-Put your thumb along the wire in the
direction of the current.
-Curl your fingers around the wire (as if
you are grasping the wire)
-Your fingers are the field lines.
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2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.
Wire #1
I1
Wire #2
I2
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2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.

B1
Wire #1
I1
Wire #2
I2
The magnetic field created by wire #1 is shown. The field points into the
page in the vicinity of wire #2, creating magnetic force upward on wire #2.
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2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.

B2
Wire #1
I1
Wire #2
I2
Now we see the field created by wire #2. The field points out of the page
in the vicinity of wire #1, creating magnetic force downward on wire #1.
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2 current-carrying wires will put magnetic forces on each other.
Wire #1 and #2 below both have current flowing to the right.
Find the direction of the magnetic force on each wire.

B2
Wire #1
I1
Wire #2
I2
Basic result:
Parallel curents - wires will attract each other
Anti-parallel currents - wires will repel.
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The field near a straight wire is curved into loops.
How can you create a straight magnetic field?
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The field near a straight wire is curved into loops.
How can you create a straight magnetic field?
Answer: Bend the wire into a loop (or lots of loops – make a coil of wire).
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The field near a straight wire is curved into loops.
How can you create a straight magnetic field?
Answer: Bend the wire into a loop (or lots of loops – make a coil of wire).
Magnetic Field in a Solenoid (aka coil)
B  0  n  I
n is the number of loops per meter
Notice the direction of the field – it looks very much like a bar
magnet. The B-field lines go in through the south pole and come
out through the north pole. Inside the coil the field is nearly
uniform and points along the axis.
To find the direction you can use a right-hand-rule:
-Curl your fingers around the coil in the direction of the current.
-Stick out your thumb: this is the direction of the B-field inside.
The strength of the field can be increased by inserting an iron core.
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Bar Magnets
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