What is the total force on any arbitrary current carrying wire in a uniform magnetic field ?

1 Answer
Sep 14, 2015

#F=BILsintheta#

Explanation:

The force on the wire is proportional to:

Current #I#

Length of wire in the field #L#

Sine of angle conductor makes with field #sintheta#

The magnetic flux density #B#

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Figure 4 shows a wire at an angle #theta#. The perpendicular vector of the magnetic field that the wire experiences will be equal to #cos(90-theta)# = #sintheta#.

The force on the wire is given by:

#F=BILsintheta#

From figure 5 you can see that if the wire is perpendicular to the field then #theta=90# and #sintheta=1#.

In this case the force is at a maximum where:

#F=BILsin90#

#=BIL#

In terms of vectors:

#F=BIstackrel(rarr)(L)#

#stackrel(rarr)(L)# is the vector from the start point to the end point. In the case of a closed loop, the wire starts and ends at the same place so:

#stackrel(rarr)(L)=0#

So:

#F=BIxx0=0#