Physics 2112Unit 15

Today’s Concept:Ampere’s Law

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Unit 15, Slide 1

Electricity & Magnetism Lecture 15, Slide 2

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We know for an infinite current carrying wire

Ampere’s Law

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But what is 2pR? Circumference of circle!

Electricity & Magnetism Lecture 15, Slide 3

Ampere’s Law

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Any closed loop

Current enclosed by that closed

loop

Checkpoint 1A

Electricity & Magnetism Lecture 15, Slide 4

Two loops are placed near identical current carrying wires as shown in Case 1 and Case 2 below.

For which loop is ∫B·dl greater? A. Case 1 B. Case 2 C. The integral is the same for

both

Checkpoint 1B

Electricity & Magnetism Lecture 15, Slide 5

Two loops are placed near identical current carrying wires as shown in Case 1 and Case 2 below.

For which loop is ∫B·dl greater? A. Case 1 B. Case 2 C. The integral is the same for

both

Checkpoint 1C

Electricity & Magnetism Lecture 15, Slide 6

Two loops are placed near current carrying wires as shown in Case 1 and Case 2 below. In both cases the direction of the current in the two wires are opposite to each other.

For which loop is ∫B·dl greater? A. Case 1 B. Case 2 C. The integral is the same for

both

Example 15.1 (B field from a thick wire)

Unit 15, Slide 7

A wire with a radius of r=1cm has a uniform current of 1A flowing through it.

What is the B field 1 meter from the center of the wire?

What is the B field 0.5cm from the center of the wire?

Example 15.1 (graph)

Unit 15, Slide 8

A wire with a radius of r=1cm has a uniform current of 1A flowing through it.

XX X X

X X X X X

XX X X

X X X X XB

r

CheckPoint 2A

Electricity & Magnetism Lecture 15, Slide 9

XAn infinitely long hollow conducting tube carries current I in the direction shown.

What is the direction of the magnetic field inside the tube?

A. clockwise B. counterclockwise C. radially inward to the center D. radially outward from the center E. the magnetic field is zero

Why is that?

Electricity & Magnetism Lecture 15, Slide 10

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Example 15.3 (Pipe of current)

An infinitely long cylindrical shell carries a uniformly distributed current of 5A out of the screen. The inner radius is a=4cm and outer radius=8cm

What is B at r = 2cm?What is B at r = 6cm?What is B at r = 16cm?

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Electricity & Magnetism Lecture 15, Slide 11

Example 15.3 (Pipe of current)

Conceptual AnalysisComplete cylindrical symmetry (can only

depend on r) can use Ampere’s law to calculate B

Strategic AnalysisCalculate B for the three regions separately: 1) r < a 2) a < r < b 3) r > b

Electricity & Magnetism Lecture 15, Slide 12

For circular path concentric with shell.

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Example 15.2 (Two thick wires)

Unit 15, Slide 13

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Two thick cables both of radius R and length L carry a current, I, side-by-side as shown to the left. The left cable has the current into the screen and the right cable has the current out of the screen.

A B C

What is the magnetic field at points A, B, C and D?- A is at the center of the left cable- B is a distance R/2 from the center of the left cable- C is at the point where the cables touch.- D is the bottom of the left cable

D

The Plan

Unit 15, Slide 14

XA B

C

What is the magnetic field at points A, B, C and D?

D

Conceptual Analysisuse Ampere’s law to calculate B from each cable separately

Strategic AnalysisNote direction of B from each cable at each point.Add B like vectors

I intoscreen

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Sign of the dot product

Electricity & Magnetism Lecture 15, Slide 15

dlB

dlB

dlB

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Ampere’s Law

Electricity & Magnetism Lecture 15, Slide 16

dl B

dl

B

dl B

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Electricity & Magnetism Lecture 15, Slide 17

Sign of the dot product

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dl B

dlB

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Electricity & Magnetism Lecture 15, Slide 18

Sign of the dot product

B Field in Solenoid

Unit 15, Slide 19

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add up

B Field in Solenoid

Unit 15, Slide 20

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X X XX

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nIB ox n = turns per unit length (Ideal Solenoid L>>>r)

Unit 15, Slide 21

Solenoid Bar Magnet

CheckPoint 2B

Electricity & Magnetism Lecture 15, Slide 22

A current carrying wire is wrapped around cardboard tube as shown below.

In which direction does the magnetic field point inside the tube?

A. left B. right C. up D. down E. out of the screen F. into the screen

Unit 15, Slide 23

Example 15.3 (B from Solenoid)

A long thin solenoid consists of 500 turns of wire carrying 1.5A. It has a length of 250cm and a radius of 1cm.

What is the magnetic field in the exact center of the coil?

What is the contribution to this field from the 250th coil (the center coil)?

Make Sense?

Unit 15, Slide 24

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X X XX

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X X XX

Note:

• B250/Btot = 0.024 (1/500 = 0.002)

• So closest coil contributes over 10 tens more than average coil. Make sense?

When does “Loop” “Solenoid”?

Electricity & Magnetism Lecture 15, Slide 25

A hint…..

Unit 15, Slide 26

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