Lesson 3.8 - Ampere's Law and Faraday's Law
VIDEO LESSON (28:50 min)
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Ampere's Law: how a current creates a magnetic field
Faraday's Law: how a magnetic field creates a current
These two laws have a natural symmetry to them that hints of the underlying nature of electromagnetism
SOLUTION:
\( B= \frac{\mu_o I}{2 \pi r} \)
\( B= \frac{(4 \pi \times 10^{-7}Tm/A)(3.0 \times 10^5 A)}{2 \pi (0.15m)} \)
\( B=0.40\) T
SOLUTION:
\( B= \frac{\mu_o NI}{L} \)
\( B= \frac{(4 \pi \times 10^{-7}Tm/A)(400)(10 A)}{2 \pi (0.20m)} \)
\( B=0.025T\) or 25 mT
The direction of the current is such that the magnetic field it produces opposes the change that produced it (Lenz's Law).
This is a product of the Law of conservation of energy. The energy gained by the current is lost by the magnet.
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ELECTROMAGNETISM
Interaction between Electricity and Magnetism:Ampere's Law: how a current creates a magnetic field
Faraday's Law: how a magnetic field creates a current
These two laws have a natural symmetry to them that hints of the underlying nature of electromagnetism
AMPERE'S LAW
Consider a uniform magnetic field perpendicular to a plane.
Consider a closed path, \(l\), through the magnetic field. The shape is arbitrary but closed
Where:
\(B_{||}\) is the component of the magnetic field parallel to the path \(\Delta l\)
\( \mu_o \) is the permeability of free space \( 4 \pi \times 10^{-7} \) Tm/A
EXAMPLE
Consider a straight wire carrying a current, \(I\), through it and for simplicity, let's consider a circular path around the wire with a radius, \(r\).EXAMPLE PROBLEM #1
What is the magnetic field strength 15cm from a straight wire with \(3.0 \times 10^5\) A flowing through it?SOLUTION:
\( B= \frac{\mu_o I}{2 \pi r} \)
\( B= \frac{(4 \pi \times 10^{-7}Tm/A)(3.0 \times 10^5 A)}{2 \pi (0.15m)} \)
\( B=0.40\) T
WHAT ABOUT A SOLENOID?
EXAMPLE PROBLEM #2
Determine the magnetic field in a solenoid carrying a current of 10A. It consists of 400 turns of copper wire over a length of 20cm.SOLUTION:
\( B= \frac{\mu_o NI}{L} \)
\( B= \frac{(4 \pi \times 10^{-7}Tm/A)(400)(10 A)}{2 \pi (0.20m)} \)
\( B=0.025T\) or 25 mT
FARADAY'S LAW
A magnetic field changing as a function time induces a current.The direction of the current is such that the magnetic field it produces opposes the change that produced it (Lenz's Law).
This is a product of the Law of conservation of energy. The energy gained by the current is lost by the magnet.
IN SUMMARY: MAXWELL'S EQUATIONS
Sửa lần cuối: Thứ sáu, 20 Tháng 6 2025, 10:28 PM