Introductory Physics Volume Two

4.6 More Examples 91
The force on this small section is:
dF ⃗ = Id⃗x × B ⃗
= (Idx)î ×
( )
ĵ
(3 T m 2
= (Idx)
(ˆk(3x 2 ) − ĵ(2x)
x 2 + ˆk
(
)
2 T m
) )
x
Integrate over the entire length of the wire to get the total force:
0.5m ∫
)
⃗F = (Idx)
(ˆk(3x 2 ) − ĵ(2x)
0
= I [ î(x 3 ) − ĵ(x 2 ) ] 0.5m
0
= (8A) [ (0.5) 3 î − (0.5) 2 ĵ ] [T · m]
= (1N)î − (2N)ĵ
Example
An L-shaped section of wire, carryies a current I, and is in a constant
magnetic field, as shown in the figure:
L 1
L 2
I
B
In terms of the parameters shown, what is the direction and magnitude
of the net magnetic force on the wire?
Use the right hand rule to find the direction of the force on each segment:
L 1
L 2
F 1
F 2
I
B