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Welcome to our Physics lesson on Another Version of Faraday's Law, this is the second lesson of our suite of physics lessons covering the topic of Induced Electric Fields, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Let's consider a positive trial charge Q0 moving around a circular path as the one shown in the figure below.
The work done by the electric field E on the test charge Q0 to make it move in a circular path as the one shown above is
where εi is the emf induced in the circular loop.
If we want to calculate the work done by the electric field to make the test charge complete one revolution only, is
where the first expression inside the brackets represents the electric force and the second the circumference of the circular path which is equal to the distance travelled by the test charge during one revolution.
Combining the last two equations, we obtain
Simplifying Q0 from both sides, we get for the induced emf
The above approach is a simplified version; it takes place only when the applied force is constant. In the general case, we use the integration method explained in tutorial 16.6. Thus, we have
(the circle in each integral is the symbol that indicates a closed path). Therefore, since the work W = Q0 ∙ εi we obtain for the induced emf in the loop:
When the last expression is combined with the standard form of Faraday's law
we obtain a new (integral) version of this law, that is
We have the following clues in this problem:
Q0 = 2 μC = 2 × 10-6 C
r = 2 cm = 0.02 m
εi = 4 kV = 0.004 V = 4 × 103 V
(π = 3.14)
a) E = ?
b) W = ?
You have reached the end of Physics lesson 16.11.2 Another Version of Faraday's Law. There are 3 lessons in this physics tutorial covering Induced Electric Fields, you can access all the lessons from this tutorial below.
|Tutorial ID||Physics Tutorial Title||Tutorial||Video|
|16.11||Induced Electric Fields|
|Lesson ID||Physics Lesson Title||Lesson||Video|
|16.11.1||Induced Electric Fields|
|16.11.2||Another Version of Faraday's Law|
|16.11.3||A New Approach on Electric Potential|
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