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Chapter 30 Ampere’s Law. PHYS 2326-19. Concepts to Know. Magnetic Forces between wires Ampere’s law Solenoid Toroid. Magnetic Forces Between Wires. Chapter 30.2 Similar to forces between two charged particles

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Presentation Transcript
concepts to know
Concepts to Know
  • Magnetic Forces between wires
  • Ampere’s law
  • Solenoid
  • Toroid
magnetic forces between wires
Magnetic Forces Between Wires
  • Chapter 30.2
  • Similar to forces between two charged particles
  • Give 2 parallel wires 1 & 2 separated by distance a with currents I1 & I2 What are the forces between them?

B2

1

I1

F1

2

I2

a

magnetic force between 2 wires
Magnetic Force Between 2 Wires
  • Wire 2 generates a field B2
  • For a long straight wire B2 is from eqn 30.5
  • Force F1 on wire 1 comes from eqn 29.10
  • Using magnitudes

eqn 30.12

Using right hand rules for directions

B2 is out of plane and F1 is down towards wire 2

ampere s law
Ampere’s Law
  • The line integral of B·ds (B dot ds) is equal to μo I (the permeability of free space times the current I)
the toroid
The Toroid
  • A ring or torus wrapped with a wire
  • Create amperian loop – dashed line
  • by symmetry (assume wire uniform all the way around) – the field is constant B and tangent to it so B·ds = B ds
  • Wire passes through N times (4 shown)
the toroid7
The Toroid
  • Since there are N turns, total current through the loop is NI
  • Apply Ampere’s law
the solenoid

.

.

.

.

.

.

.

x

x

x

x

x

x

The Solenoid
  • Ideal solenoid is when length >> radius
  • B is uniform and parallel inside ideal solenoid
  • Consider loop 2 a rectangle w*l in area
  • Side 3 is far away so B = 0, side 2&4 B is perpendicular with the sides
  • Side 1 is parallel and in a uniform field B so that the magnitude is Bl

B

loop 2

2

3

l

1

4

w

loop 1

example 1
Example 1
  • Given a rectangular loop of 10cm x 20cm (a by b) with counter clockwise current I=2A what is the magnitude and direction of magnetic field at the center point P
  • B direction right hand rule = out of page
  • B = Bab+Bbc+Bcd+Bda = 2Bab + 2Bbc

a

d

I

P

b

c

example 110
Example 1

From eqn 30.4 for the field produced by a long wire. The book shows sines which is opposite/adjacent

  • B = 8.78E-6 T
example 2
Example 2
  • Long straight vertical wire carries 10A

A rectangular coil of wire located near it carries 5 A, a = 0.10m, b=0.30m, c=0.50m. Force on loop?

Force on top = -Force on bottom

b

c

I2

I1

a

x

example 3
Example 3

Use Ampere’s Law to determine magnetic field

Choose a circle centered around the wire so B is tangent at every point and uniform in distance from the wire

B

dl

r

I

example 314
Example 3
  • Dot product B·l = Bdl
  • Same magnitude at each point (symmetry)
  • B is constant so
example 4 inside and outside a toroid
Example 4Inside and outside a Toroid
  • Find the magnetic field a) inside and b) outside a tightly wound toroid of N turns