Environmental Engineering Reference
In-Depth Information
Fig. 3.4 a An electric circular loop carrying a current I and placed in the uniform magnetic eld,
b forces acting on the electric loop in the uniform magnetic eld
dF
l
0
H
¼
I d
~
s
ð
3
:
17
Þ
If we now consider an electric circular loop carrying a current I and placed in a
uniform magnetic
eld, the net force on such a loop will be zero (Fig.
3.4
).
However, this will not hold true for the magnetic torque:
dT
¼
r
dF
¼
r
Id
s
l
0
H
ð
3
:
18
Þ
In Fig.
3.4
, four forces are acting on the coils, two of which are equal in
magnitude but opposite in direction (F
1
and F
3
, and F
2
and F
4
respectively). It
follows that:
X
4
F
i
¼
F
1
þ
F
2
þ
F
3
þ
F
4
¼
0
ð
3
:
19
Þ
1
The forces F
1
and F
3
do not contribute to the torque, however, by F
2
and F
4
,a
torque acts on the coil.
If we focus on the two forces that contribute to the torque (Fig.
3.5
), then it
follows that:
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