Shrinking Loop. A circular loop of flexible iron wire has an initial circumference of 167 cm, but its circumference is decreasing at a constant rate of 10.0 cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 0.600 T, which is oriented perpendicular to the plane of the loop.
Find the (magnitude of the) emf EMF induced in the loop after exactly time 1.00 s has passed since the circumference of the loop started to decrease.
im pretty sure ive been doing it right but as usual probaly a dumb mistake.
it all looks right and what i did also. yet it seems like the answer should be larger because whenever i input it into the program it seems like its too small because it says the flux should occur since the area is changing. It seems to be taking it as zero. we converted it to meters so it should be ok.
nvm dangit it works. just off by a small amount.
Spencer is wrong. Just so you guys know
@drwls math mustve been different in 2008 because i have no idea what you did
To find the magnitude of the induced electromotive force (emf) in the loop after 1.00 second, we can use Faraday's law of electromagnetic induction. This law states that the emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit.
First, let's calculate the initial magnetic flux through the loop. The magnetic flux is given by the product of the magnetic field (B) and the area (A) enclosed by the loop.
The initial circumference of the loop is 167 cm, so its radius (r_initial) can be calculated by dividing the circumference by 2π:
r_initial = 167 cm / (2π) ≈ 26.60 cm
The initial area (A_initial) of the loop is given by the formula for the area of a circle:
A_initial = π * (r_initial)^2
Now, let's calculate the magnetic flux (Φ_initial) through the loop:
Φ_initial = B * A_initial
Next, we need to find the final area (A_final) of the loop after 1.00 second has passed. Since the circumference is decreasing at a constant rate of 10.0 cm/s, the radius of the loop at t = 1.00 second can be calculated as:
r_final = r_initial - (rate of decrease * time)
r_final = 26.60 cm - (10.0 cm/s * 1.00 s)
Finally, we can calculate the final area of the loop (A_final) using the new radius:
A_final = π * (r_final)^2
Now, we can calculate the rate of change of magnetic flux (dΦ/dt) by subtracting the initial flux from the final flux and dividing by the time taken:
dΦ/dt = (Φ_final - Φ_initial) / t
Finally, the magnitude of the induced emf (EMF) is given by:
EMF = -dΦ/dt
The negative sign indicates that the direction of the induced current opposes the change in magnetic flux.
By following these steps and plugging in the appropriate values, you should be able to calculate the magnitude of the induced emf in the loop after 1.00 second.
Area A is related to circumference C by
A = pi r^2 = pi * [C/(2 pi)]^2
= [1/(4 pi)]C^2
C = 1.67 - 0.1 t (in meters)
dA/dt = [1/(2 pi)] C dC/dt
= -(0.05/pi) C
V(t) = B*dA/dt = B (0.05/pi) C(t)
With B in Tesla, the answer will be in volts. Choose t = 1 second to get C. I have thrown out the minus sign, since we don't care about polarity
Check my math and thoughts. No guarantees here.