Introductory Physics Volume Two

90 Magnetic Fields 4.6
+e
v = ?
r
L = 10cm
B = 0.3T
Let’s compute the radius of the path in terms of the velocity. Newton’s
second law applied to the proton yields
F B = m v2
r
evB = m v2
r
−→ r = mv
eB
So as v increases so does r. In order that the proton not exit through
the other side of the magnetic field region we must have r < L;
mv
eB < L
−→ v < eBL
m
= 2.9 × 106 m s
Example
A straight section of wire that is 0.5m long and carrying a current of
I = 8A directed along the +x axis. One end of the wire is at the origin
. The wire is in a magnetic field
⃗B = ĵ
(3 T m 2 )
x 2 + ˆk
What is the force on the wire?
Look at a small section of the wire:
y
( )
2 T x.
m
x
dx
x
z