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27. Magnetic Field and Magnetic Forces
Assignment is due at 2:00am on Wednesday, February 28, 2007
Credit for problems submitted late will decrease to 0% after the deadline has passed.
The wrong answer penalty is 2% per part. Multiple choice questions are penalized as described in the online help.
The unopened hint bonus is 2% per part.
You are allowed 4 attempts per answer.
Forces on moving charges and currents in Magnetic Field
Force on Moving Charges in a Magnetic Field
Learning Goal:
To understand the force on a charge moving in a magnetic field.
Magnets exert forces on other magnets even though they are separated by some distance. Usually the force on a
magnet (or piece of magnetized matter) is pictured as the interaction of that magnet with the
magnetic field
at its
location (the field being generated by other magnets or currents). More fundamentally, the force arises from the
interaction of individual moving charges within a magnet with the local magnetic field. This force is written
, where
is the force,
is the individual charge (which can be negative),
is its velocity, and
is the
local magnetic field.
This force is nonintuitive, as it involves the vector product (or cross product) of the vectors
and
. In the
following questions we assume that the coordinate system being used has the conventional arrangement of the axes,
such that it satisfies
, where
,
, and
are the unit vectors along the respective axes.
Let's go through the righthand rule. Starting with the generic vector crossproduct equation
point your
forefinger of your right hand in the direction of
, and point your middle finger in the direction of
. Your thumb
will then be pointing in the direction of
.
Part A
Consider the specific example of a positive charge
moving in the +
x
direction with the local magnetic field in
the +
y
direction. In which direction is the magnetic force acting on the particle?
Express your answer using unit vectors (e.g.,

). (Recall that
is written
x_unit
.)
ANSWER:
Direction of
=
Part B
Now consider the example of a positive charge
moving in the +
x
direction with the local magnetic field in the
+
z
direction. In which direction is the magnetic force acting on the particle?
Express your answer using unit vectors.
ANSWER:
Direction of
=
Part C
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Now consider the example of a positive charge
moving in the
xy
plane with velocity
(i.e.,
with magnitude
at angle
with respect to the
x
axis). If the local magnetic field is in the +
z
direction, what is
the direction of the magnetic force acting on the particle?
Hint C.1 Finding the cross product
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