g) Show the time rate of change in the magnetic flux is d$m(x) _ _Ho'l •a ·b• V [ dt [9 + x) • x. h) Use Faradays Law to determine the induced EMF at x = 3cm
g) Show the time rate of change in the magnetic flux is d$m(x) _ _Ho'l •a ·b• V [ dt [9 + x) • x. h) Use Faradays Law to determine the induced EMF at x = 3cm
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Question
Please answer G, H. Thank you
![The following picture shows a LONG conductor carrying current I. Nearby there is a
conducting rectangular loop with sides a = 8 cm and b = 4 cm. The loop also caries a
resistance R = 10 ohms. The curent is constant and has a value of I = 6.0 Amperes. The
loop is moving away to the right with a constant velocity, V = 2 m/s. Answer the following
questions at the instant of time t' when the left edge of the loop is at position x" as shown
below
Use the coordinate system , x to the right, y into the board, z upward
a) Write an expression for the magnetic field as a function of
the distance "x" (from the LONG conductor to the loop. )
USE “+" for CCW circulation and "-“ for CW circulation.
b) Write the magnetic field in "i-j-k" format at point "x"to the
right of the current carrying wire in the "i-z" plane
c) Write the infinitesimal area vector for the loop in "i-j-k"
format
d) Write the explicit integral for the magnetic flux through the
area of the loop using the answer for B and dA above.
Include limits on the area integral In general
= || 5 - aa
e) Integrate the flux integral above to obtain
„(x) = 40""[In(x + b) – In(x)]
f) Express the position "x" as a function of r
g) Show the time rate of change in the magnetic flux is
d®m(x) _ _Ho•I •a·b•V[
dt
x-(x+ b)]
h) Use Faradays Law to determine the induced EMF at x = 3cm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d7f8ba3-ac35-40be-9d69-f75baa192b25%2Fde1b7590-ffcc-473a-8178-8b56bdbb09bd%2F2gl6gn_processed.png&w=3840&q=75)
Transcribed Image Text:The following picture shows a LONG conductor carrying current I. Nearby there is a
conducting rectangular loop with sides a = 8 cm and b = 4 cm. The loop also caries a
resistance R = 10 ohms. The curent is constant and has a value of I = 6.0 Amperes. The
loop is moving away to the right with a constant velocity, V = 2 m/s. Answer the following
questions at the instant of time t' when the left edge of the loop is at position x" as shown
below
Use the coordinate system , x to the right, y into the board, z upward
a) Write an expression for the magnetic field as a function of
the distance "x" (from the LONG conductor to the loop. )
USE “+" for CCW circulation and "-“ for CW circulation.
b) Write the magnetic field in "i-j-k" format at point "x"to the
right of the current carrying wire in the "i-z" plane
c) Write the infinitesimal area vector for the loop in "i-j-k"
format
d) Write the explicit integral for the magnetic flux through the
area of the loop using the answer for B and dA above.
Include limits on the area integral In general
= || 5 - aa
e) Integrate the flux integral above to obtain
„(x) = 40""[In(x + b) – In(x)]
f) Express the position "x" as a function of r
g) Show the time rate of change in the magnetic flux is
d®m(x) _ _Ho•I •a·b•V[
dt
x-(x+ b)]
h) Use Faradays Law to determine the induced EMF at x = 3cm
Expert Solution
Step 1
Faraday's Law of Electromagnetic Induction
- Whenever there is a change in magnetic flux linked to a coil, an emf is induced in the coil.
- The induced emf is equal to the rate of change of magnetic flux.
Lenz's Law
The direction of the induced emf is such that it opposes the very cause for which it has been formed.
If is the change in magnetic flux in time then the induced emf is
Step 2
g) In question (e) you have found that the magnetic flux linked to the rectangular loop is
Taking the time derivative of the magnetic flux
is the velocity of the rectangular loop.
h) Now from Faraday's Law we know that the induced emf
Using the data given in the question, at , the induced emf is
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