1. Physics 212
Lecture 14
Biot-Savart Law
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2. Infinite Straight Wire
Biot-Savart Law:
We can use this law to calculate the magnetic field produced by ANY current distribution
BUT
Easy analytic calculations are possible only for a few distributions:
Infinite Straight Wire
Axis of Current Loop
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3. Field at the center of a ringP
points out of page for each

4. B from infinite line of current
Magnitude: B
Current I OUT r •
r = distance from wire
Direction:
Thumb: on I
Fingers: curl in direction of B
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5. Currents + Charges • • |Fa |> |Fb| |Fa |= |Fb| |Fa |< |Fb|
A long straight wire is carrying current from left to right. Two identical charges are moving with equal speed. Compare the magnitude of the force on charge a moving directly to the right, to the magnitude of the force on charge b moving up and to the right at the instant shown (i.e. same distance from the wire). v v • B
Forces are in different directions • F
(a)
(b) r r I
|Fa |> |Fb|
|Fa |= |Fb|
|Fa |< |Fb|
Same q, |v|, B and q (=90) 28
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6. Comment on making T for direction, then decide which way is correct
Magnetic Fields obey superposition B x
Two long wires carry equal and opposite currents x
Comment on making T for direction, then decide which way is correct
What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”?
A) Left B) Right C) Up D) Down E) Zero
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7. Maybe circle muI1/2pid as B?
Force between current-carrying wires B d • • I2 I1 F
Conclusion: Currents in same direction attract. • I1 B d F  I2
Maybe circle muI1/2pid as B?
Conclusion: Currents in opposite direction repel.
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8. Uniform force at every segment of wire
Checkpoint 1 X B F
What is the direction of the force on wire 2 due to wire 1?
A) Up B) Down C) Into Screen D) Out of screen E) Zero
What is the direction of the torque on wire 2 due to wire 1?
A) Up B) Down C) Into Screen D) Out of screen E) Zero
Draw B and F arrows
Uniform force at every segment of wire
No torque about any axis
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9. Checkpoint 3a
What is the direction of the force on wire 2 due to wire 1?
A) Up B) Down C) Into Screen D) Out of screen E) Zero
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10. Consider Force on Symmetric Segments!B I
F out of screen I
F into screen B r r
Net Force is Zero!
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11. Checkpoint 3b B i F out of screen F into screen
What is the direction of the torque on wire 2 due to wire 1?
A) Up B) Down C) Into Screen D) Out of screen E) Zero B i
F out of screen
F into screen
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12. Draw forces on each segment
Checkpoint 2
A current carrying loop of width a and length b is placed near a current carrying wire. How does the net force on the loop compare to the net force on a single wire segment of length a carrying the same amount of current placed at the same distance from the wire?
Draw forces on each segment
The forces are in opposite directions
The net forces are the same
The net force on the loop is greater than the net force on the wire segment
The net force on the loop is smaller than the net force on the wire segment
There is no net force on the loop A B C D E
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13. Draw forces on each segment
Checkpoint 2
A current carrying loop of width a and length b is placed near a current carrying wire. How does the net force on the loop compare to the net force on a single wire segment of length a carrying the same amount of current placed at the same distance from the wire?
Ftop + Fbottom =0 X B1 X B2 X B1 F2
B ~ 1/R
B1 > B2 F1
Fnet
Draw forces on each segment
The forces are in opposite directions
The net forces are the same
The net force on the loop is greater than the net force on the wire segment
The net force on the loop is smaller than the net force on the wire segment
There is no net force on the loop A B C D E
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14. B on axis from Current Loop
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15. Biot-Savart works, but need to do numerically
What about Off-Axis ??
Biot-Savart works, but need to do numerically
See Simulation !!
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16. Direction of B reverses
Magnetic field of a dipole moment
Direction of B reverses
from inside to outside.
B gets weaker
S N

17. Two Current Loops
Two identical loops are hung next to each other. Current flows in the same direction in both.
The loops will:
A) Attract each other B) Repel each other
Two ways to see this:
Like currents attract N S
2) Look like bar magnets
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18. Right Hand Rule Review 1. ANY CROSS PRODUCT
2. Direction of Magnetic Moment
Thumb: Magnetic Moment
Fingers: Current in Loop
3. Direction of Magnetic Field from Wire
Thumb: Current
Fingers: Magnetic Field 06

19. Calculation
Two parallel horizontal wires are located in the vertical (x,y) plane as shown. Each wire carries a current of I =1A flowing in the directions shown.
What is the B field at point P? y y
I1=1A .
4cm
3cm x z
4cm P
I2=1A
Front view
Side view
(A) (B) (C) (D) (E) y . z P
What is the direction of B at P produced by the top current I1?
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
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20. Calculation
Two parallel horizontal wires are located in the vertical (x,y) plane as shown. Each wire carries a current of I =1A flowing in the directions shown.
What is the B field at point P? y y
I1=1A .
4cm
3cm x z
4cm P
I2=1A
Front view
Side view
What is the direction of B at P produced by the bottom current I2? . z y P
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
(A) (B) (C) (D) (E)
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21. Calculation . . . What is the direction of B at P? (A) (B) (C) (D)
Two parallel horizontal wires are located in the vertical (x,y) plane as shown. Each wire carries a current of I =1A flowing in the directions shown.
What is the B field at point P? y y
I1=1A .
4cm
3cm x z
4cm P
I2=1A
Front view
Side view
What is the direction of B at P?
(A) (B) (C) (D) . z y P . y
90o
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. z P
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22. Calculation
Two parallel horizontal wires are located in the vertical (x,y) plane as shown. Each wire carries a current of I =1A flowing in the directions shown.
What is the B field at point P? y y
I1=1A .
4cm
3cm x z
4cm P
I2=1A
Front view
Side view
What is the magnitude of B at P produced by the top current I1? (m0 = 4p x 10-7 T-m/A)
(A) 4.0 x 10-6 T (B) 5.0 x 10-6 T (C) 6.7 x 10-6 T
3cm z y .
4cm r
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
What is r?
r = distance from wire axis to P
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23. Calculation
Two parallel horizontal wires are located in the vertical (x,y) plane as shown. Each wire carries a current of I =1A flowing in the directions shown.
What is the B field at point P? y y
I1=1A .
4cm
3cm x z
4cm P
Btop = 4 X 10-6 T
I2=1A
Front view
Side view
What is the magnitude of B at P? (m0 = 4p x 10-7 T-m/A)
(A) 3.2 x 10-6 T (B) 4.8 x 10-6 T (C) 6.4 x 10-6 T (D) 8.0 x 10-6 T y .
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
5cm q q B1
4cm z q B2
3cm
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