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![. 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 carries 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 carying wire in the "-z" plane
R
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
e) Integrate the flux integral above to obtain
„(x) = "
Ho`I-a[in(x+b) – In(x)]
f) Express the position "x" as a function of "
g) Show the time rate of change in the magnetic flux is
do„(x) _ _Ho·I•a ·b•V[_
dt
(q + x) . x
h) Use Faradays Law to determine the induced EMF at x = 3cm
i) Use Ohms Law to detemine the current in the loop when x = 3cm
i) Use Lenz's Law to determine which direction does the current flow? (Clock Wise or Counter
Clock Wise). Explain.
NOTE: Lenz's Law says the direction of the induced current will create a magnetic field to
oppose the original change in the magnetic flux. That is, if the original magnetic flux through
the loop is increasing, the direction of the INDUCED magnetic field is opposite the original
magnetic field. Similarly, if the original magnetic flux through the loop is decreasing, the
direction of the INDUCED magnetic field is in the same direction the original magnetic field.)](https://content.bartleby.com/qna-images/question/7d7f8ba3-ac35-40be-9d69-f75baa192b25/7c0f315d-797c-4dab-906a-d1caab1e52d4/mfh4fz8_processed.png)
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 carries 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 carying wire in the "-z" plane
R
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
e) Integrate the flux integral above to obtain
„(x) = "
Ho`I-a[in(x+b) – In(x)]
f) Express the position "x" as a function of "
g) Show the time rate of change in the magnetic flux is
do„(x) _ _Ho·I•a ·b•V[_
dt
(q + x) . x
h) Use Faradays Law to determine the induced EMF at x = 3cm
i) Use Ohms Law to detemine the current in the loop when x = 3cm
i) Use Lenz's Law to determine which direction does the current flow? (Clock Wise or Counter
Clock Wise). Explain.
NOTE: Lenz's Law says the direction of the induced current will create a magnetic field to
oppose the original change in the magnetic flux. That is, if the original magnetic flux through
the loop is increasing, the direction of the INDUCED magnetic field is opposite the original
magnetic field. Similarly, if the original magnetic flux through the loop is decreasing, the
direction of the INDUCED magnetic field is in the same direction the original magnetic field.)
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