solution to quiz4
1. An electron enters a region of magnetic field of magnitude 0.01 T, traveling perpendicular to the linear
boundary of the region.
The direction of the field is perpendicular to the velocity of the electron.
Determine the time it takes for the electron to leave the “fieldfilled” region, noting that its path is a
semicircle.
Answer:
1.8 ns
hint:
The Lorentz force serves as a centripetal force,
F
=
evB
=
mv
2
r
⇒
r
=
mv
eB
so the time it takes to complete a semicircle is
t
=
πr
v
=
πm
eB
= 1
.
8
ns
2. Find the direction of the force on a proton if its velocity and the field are shown as in Figure 1.
Answer:
a:
←
, b:
⊗
, c:
, d:
↑
, e:
⊗
, f:
hint:
Direction of force is determined by direction of
~v
×
~
B
(for negative charges, will be the opposite),
and direction of cross product in turn is determined by the right hand rule, e.g., ˆ
x
×
ˆ
y
= ˆ
z
, instead of

ˆ
z
.
3. A thin, horizontal copper rod is 1.00 m long and has a mass of 50.0 g. What is the minimum current
in the rod that can cause it to float in a horizontal magnetic field of 2.00 T?
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 Winter '07
 BRIANKEATING
 Magnetic Field, Righthand rule

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