Unformatted text preview: re loop to do mechanical work.
By running current through the loop immersed in
a magnetic field we can rotate the loop. Physics 2B  Summer Session 2  C. Palmer August 26, 2013 21 y There is a rectangular loop
(sides w, l) of current, I.
What is the force on each
side?
What is the torque? ˆ
B = B0 x
2
I z y x 3 1
4 x l w
Physics 2B  Summer Session 2  C. Palmer August 26, 2013 22 y There is a rectangular loop
(sides w, l) of current, I.
What is the force on each
side?
The force on side 2 and 4 is
0. ˆ
B = B0 x
2
I z y x 3 1
4 x l w
Physics 2B  Summer Session 2  C. Palmer August 26, 2013 23 y There is a rectangular loop
(sides w, l) of current, I.
What is the force on each
side?
The force on side 1 and 3
will be in opposite
direction and equal in
magnitude. ˆ
B = B0 x
2
I y x 3 1 Physics 2B  Summer Session 2  C. Palmer z 4 x l w
August 26, 2013 24 y There is a rectangular loop
(sides w, l) of current, I.
What is the force on each
side? ˆ
F1 = IlB0 ( − z ) ˆ
F3 = IlB0 ( + z ) ˆ
B = B0 x
2
I Physics 2B  Summer Session 2  C. Palmer y x 3 1 Total force is 0. z 4 x l w
August 26, 2013 25 z Flip the coordinate
system to see the forces
better.
Recall torque: τ =r ×F What is the torque about
the origin? y x F
r1 r2 3
I I F1 ˆ
F1 = IlB0 ( − z ) ˆ
F3 = IlB0 ( + z ) Physics 2B  Summer Session 2  C. Palmer August 26, 2013 26 z What is the torque about
the origin? τ = r F sin θ x y F3 θ r1 I r2 I θ
F1 ˆ
F1 = IlB0 ( − z ) ˆ
F3 = IlB0 ( + z ) Physics 2B  Summer Session 2  C. Palmer August 26, 2013 27 z What is the torque about
the origin? w
ˆ
τ 1 = IlB0 sin θ ( − y )
2
w
ˆ
τ 3 = IlB0 sin θ ( − y )
2 ˆ
τ Total = IlwB0 sin θ ( − y ) x y F3 θ r1 I r2 I θ
F1 ˆ
F1 = IlB0 ( − z ) ˆ
F3 = IlB0 ( + z ) Physics 2B  Summer Session 2  C. Palmer August 26, 2013 28 z ˆ
τ Total = IlwB0 sin θ ( − y ) y F3 θ ˆ
= I ( Area ) B0 sin θ ( − y )
r1 Same torque
I r2 I From anywhere inside
θ
the wire loop
F1 x For arbitrary shaped loopalways area
To keep the rotation going in the same direction one
can alternate the current Physics 2B  Summer Session 2  C. Palmer August 26, 2013 29 ˆ
τ = I ( Area ) B0 sin θ ( − y ) ˆ
= ( IAn ) × B = µ × B
This motivates defining a vector with is the current times area of a
loop.
The direction is given by curling
the fingers of your right hand in
the direction of the current.
Your thumb points in the direction of µ.
Physics 2B  Summer Session 2  C. Palmer August 26, 2013 30 τ =µ×B U = −µ ⋅ B
The torque tends to make the
magnetic dipole
moment point in
the direction of
the magnetic
field. Physics...
View
Full
Document
This note was uploaded on 09/10/2013 for the course PHYS 2B 2b taught by Professor Hirsch during the Summer '10 term at UCSD.
 Summer '10
 Hirsch

Click to edit the document details