Download Week 11 Monday

Lecture 3/27/2017
• Magnetic force on a moving charge.
• Motion of charged particles in magnetic
fields.
• Torque on a current loop.
Force on an Electric Charge Moving in a
Magnetic Field
The force on a moving charge is related to
the force on a current:
Once again, the
direction is given by
a right-hand rule.
A proton beam enters a
magnetic field region as shown
below. What is the direction of
the magnetic field B?
1) + y
2) – y
3) + x
4) + z (out of page)
5) – z (into page)
y
x
A electron beam enters a
magnetic field region as shown
below. What is the direction of
the magnetic field B?
1) + y
2) – y
3) + x
4) + z (out of page)
5) – z (into page)
y
x
Force on an Electric Charge Moving in a
𝒃
Magnetic Field
𝑾 = න 𝑭 ∙ 𝒅𝒔
𝒂
If a charged particle is
moving perpendicular
to a uniform magnetic
field, its path will be a
circle.
Does the magnetic
force do work on the
charge?
a)Yes
b)No
A proton moves in a circular orbit of radius 14cm
in a uniform 0.35T magnetic field perpendicular
to the velocity of the proton.
Find the speed of the proton in Mm/s.
𝒎𝒑𝒓𝒐𝒕𝒐𝒏 = 𝟏. 𝟔𝟕 × 𝟏𝟎−𝟐𝟕 𝒌𝒈
Force on an Electric Charge Moving in a
𝒃
Magnetic Field
𝑾 = න 𝑭 ∙ 𝒅𝒔
𝒂
If a charged particle is
moving perpendicular
to a uniform magnetic
field, its path will be a
circle.
Does the magnetic
force do work on the
charge?
a)Yes
b)No
Force on an Electric Charge Moving in a
Magnetic Field
Can a magnetic field be used to stop a single
charged particle, as an electric field can?
A) Yes
B) No
C) Depending on which direction the charge
is moving with respect to the magnetic
field.
Force on an Electric Charge Moving in a
Magnetic Field
What is the path of a charged particle in a
uniform magnetic field if its velocity is not
perpendicular to the magnetic field?
Force on an Electric Charge Moving in a
Magnetic Field
𝒗 𝒘𝒉𝒆𝒏 𝑭𝑬 = −𝑭𝑩
𝑬
𝒗=
𝑩
The Hall Effect
When a current-carrying wire
is placed in a magnetic field,
there is a sideways force on
the electrons in the wire. This
tends to push them to one
side and results in a potential
difference from one side of the
wire to the other; this is called
the Hall effect. The emf differs
in sign depending on the sign
of the charge carriers; this is
how it was first determined
that the charge carriers in
ordinary conductors are
negatively charged.
The Hall Effect
If d is the width of the
conductor the Hall voltage is:
𝑉𝐻 = 𝐸𝐻 𝑑 = 𝑣𝑑 𝐵𝑑
Recall:
𝐼
𝑣𝑑 =
𝑛𝑞𝐴
Then we can write (in terms of
the current):
𝐼𝐵𝑑
𝑉𝐻 =
𝑛𝑞𝐴
A rectangular copper strip 1.5 cm wide and
0.10 cm thick carries a current of 5.0 A. Find
the Hall voltage (in µV) for a 1.2 T magnetic
field applied in a direction perpendicular to
the strip.
𝐼𝐵𝑑
𝑉𝐻 =
𝑉𝐻 = 𝐸𝐻 𝑑 = 𝑣𝑑 𝐵𝑑
𝑛𝑞𝐴
Torque on a Current Loop; Magnetic Dipole
Moment
The forces on opposite sides of
a current loop will be equal and
opposite (if the field is uniform
and the loop is symmetric), but
there may be a torque.
The magnitude of the torque is
given by
Torque on a Current Loop; Magnetic Dipole
Moment
The quantity NIA is called the magnetic
dipole moment, μ:
We can rewrite the torque as:
𝝉=𝝁×𝑩
The potential energy of the loop
depends on its orientation in the field:
At the Large Hadron Collider in Geneva
Switzerland, protons having a momentum of
3.75 x 10-15 kg m/s (7 TeV/c) are held in a circular
with a circumference of 27 km by an upward
magnetic field.
𝒎𝒑𝒓𝒐𝒕𝒐𝒏 = 𝟏. 𝟔𝟕 × 𝟏𝟎−𝟐𝟕 𝒌𝒈
What is the magnitude of this field?