Unit 4 – Magnetism and Electromagnetic Induction
Unit 4 – Magnetism and Electromagnetic Induction
◦ Section 1 – Magnetic Fields and Forces: 20-1, -2, -3, -4, -5
◦ Section 2 – Electromagnetic Induction: 21-1, -2, -3
Warm-up
• An alpha particle, mass 6.68 x 10-27 kg and charge +3.2 x 10-19 C.
The particle is traveling at 5.0 x 107 m/s and enters a magnetic
field of magnitude 0.20 T. The magnetic field is directly out of
the page and the alpha particle is moving directly to the right.
a) Determine the radius of the circle in which the particle
travels.
b) Determine the direction of motion in which the particle
travels (clockwise or counterclockwise).
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Electromagnetic Induction
◦ Faraday tested whether a magnet could induce current flow.
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Electromagnetic Induction
◦ Faraday determined that a magnetic field cannot induce a current
◦ BUT, a change in a magnetic field can induce a current
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Magnetic Flux (FLOW)
◦ In order to determine the change in a magnetic field, we must
define a magnetic field per a unit of area.
Magnetic Flux: 𝚽 𝑩 = 𝑩 ∙ 𝑨
or
𝚽 𝑩 = 𝑩 ∙ 𝒄𝒐𝒔𝜽 ∙ 𝑨
◦ 𝚽 𝑩 : Magnetic Flux, units – Weber (Wb) = V·s
◦ 𝑩: Magnetic Field, units – T
◦ 𝑨: Area, units – m2
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Magnetic Flux: 𝚽 𝑩 = 𝑩 ∙ 𝑨
or
𝚽 𝑩 = 𝑩 ∙ 𝒄𝒐𝒔𝜽 ∙ 𝑨
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Magnetic Flux: 𝚽 𝑩 = 𝑩 ∙ 𝑨
or
𝚽 𝑩 = 𝑩 ∙ 𝒄𝒐𝒔𝜽 ∙ 𝑨
Example 21-2: A square loop of wire 10.0 cm on a side is in a
1.25 T magnetic field B. What are the maximum and
minimum values of flux that can pass through the loop?
What changes to get these two values?
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Faraday’s Law: a change in magnetic field over time
Formula:
𝛆=
∆𝚽 𝑩
−
∆𝒕
◦ 𝜺: emf (electric potential), units – V
◦ 𝚽 𝑩 : Magnetic Flux, units – Weber (Wb) = V∙s
◦ ∆𝒕: change in time, units – s
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Coil: closely wrapped loops of wire
Formula:
𝛆=
∆𝚽 𝑩
−𝑵
∆𝒕
◦ 𝑵: Number of loops, unit-less
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Faraday’s Law: a change in magnetic field over time
How do we change the magnetic field over time?
1. Changing a Magnetic Field (B)
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
How do we change the magnetic field over time?
2. Changing the Area of the loop in the field
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
How do we change the magnetic field over time?
3. Changing the loops orientation to the field
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Faraday’s Law:
𝛆=
∆𝚽 𝑩
−
∆𝒕
Example 21-5: A square coil of wire with side l = 5.00 cm contains 100
loops and is positioned perpendicular to a uniform 0.600 T magnetic
field (directed into the paper). It is quickly pulled from the field (moving
perpendicular to B) to a region where B drops to zero. It takes 0.100 s
for the entire coil to reach the field free area. The coil’s total resistance
is 100 Ω.
a) What is the induced emf?
b) What is the induced current?
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Lenz’s Law:
An induced electromotive force (emf) always gives rise to a
current whose magnetic field opposes the original change in
magnetic flux
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Lenz’s Law: The induced magnetic field inside any loop of wire always acts to
keep the magnetic flux in the loop constant. In the examples below, if the B field is
increasing, the induced field acts in opposition to it. If it is decreasing, the induced
field acts in the direction of the applied field to try to keep it constant.
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Lenz’s Law: Giancoli Rule
1. The magnetic field due to the induced current:
a) Points in the same direction as the external field if the flux is decreasing
b) Points in the opposite direction as the external field if the flux is increasing
c) Is zero if the flux is not changing
2. Once you know the direction of the induced magnetic field, use the Right Hand
Rule to find the direction of the induced current.
Example: P. 588 Giancoli
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Lenz’s Law and Conservation of Energy
MIT Demo : Lenz Law
Warm-up
1. Suppose the induced electromotive force of a
double loop wire has a magnitude of 1.1V when
the change in magnetic flux is 0.683T•m2. How
much time has elapsed for the flux change?
2. If an electric wire is allowed to produce a
magnetic field no larger than that of the Earth
(0.55 × 10−4 𝑇) at a distance 25 cm away from
it, what is the maximum current the wire can
carry?
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
EMF Induced in a Moving Conductor
◦ Magnetic Force and Right Hand Rule cause an emf to form in a
moving conductor
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
Separation of Charges
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
EMF Induced in a Moving Conductor
◦ Formula: 𝜀 = 𝐵ℓ𝑣
Unit 4 – Magnetism and Electromagnetic Induction
Section 2 – Electromagnetic Induction
EMF Induced in a Moving Conductor: 𝜀 = 𝐵ℓ𝑣
Example 21-6: An airplane travels 1000 km/h in a region
where the Earth’s magnetic field is 5.0 x 10-5 T and is nearly
vertical. What is the potential difference induced between the
wing tips that are 70 m apart?