A circular loop in the plane of a paper lies in a 0.55 TT magnetic field pointing into the paper. The loop's diameter changes from 17.0 cmcm to 5.6 cmcm in 0.52 ss .Part APart completeWhat is the direction of the induced current?counterclockwiseclockwiseSubmitPrevious Answers CorrectPart BWhat is the magnitude of the average induced emf?
Question
A circular loop in the plane of a paper lies in a 0.55 TT magnetic field pointing into the paper. The loop's diameter changes from 17.0 cmcm to 5.6 cmcm in 0.52 ss .Part APart completeWhat is the direction of the induced current?counterclockwiseclockwiseSubmitPrevious Answers CorrectPart BWhat is the magnitude of the average induced emf?
Solution
Part A: The direction of the induced current can be determined using Lenz's Law, which states that the induced current will always work to oppose the change in magnetic flux that produced it. In this case, the magnetic field is pointing into the paper and the area of the loop is decreasing. This means the magnetic flux through the loop is decreasing. To oppose this change, the induced current will create a magnetic field that also points into the paper. Using the right-hand rule, we can determine that the direction of the induced current is counterclockwise.
Part B: The magnitude of the average induced emf can be calculated using Faraday's Law of electromagnetic induction, which states that the induced emf is equal to the rate of change of magnetic flux.
The magnetic flux (Φ) through the loop is given by the product of the magnetic field strength (B), the area of the loop (A), and the cosine of the angle between the field and the normal to the loop (cosθ). In this case, the magnetic field is perpendicular to the loop, so cosθ = 1.
The area of the loop is changing from π*(17 cm/2)^2 to π*(5.6 cm/2)^2, so the change in area (ΔA) is π*(17 cm/2)^2 - π*(5.6 cm/2)^2.
The change in flux (ΔΦ) is then B*ΔA.
The rate of change of flux (dΦ/dt) is ΔΦ/Δt, where Δt is the time it takes for the loop to change size (0.52 s).
The magnitude of the average induced emf is then |dΦ/dt|.
So, you just need to plug in the given values into these equations to find the magnitude of the average induced emf.
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