Environmental Engineering Reference
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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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