How to find the maximum induced current for a diamond-shaped loop?

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SUMMARY

The discussion focuses on calculating the maximum induced current for a diamond-shaped metal loop moving at 10 m/s in a uniform magnetic field of 0.8 T. The relevant equations include emf = -dΦB/dt and ΦB = ∫B*dA, with the area of the diamond defined as A = (1/2)bh. Participants express confusion regarding the differences in induced current behavior between the diamond-shaped loop and a square loop, particularly why the induced current decreases when the diamond loop is halfway in the magnetic field, despite similar areas.

PREREQUISITES
  • Understanding of electromagnetic induction principles
  • Familiarity with Faraday's Law of Induction
  • Knowledge of magnetic flux calculations
  • Basic geometry of shapes, specifically diamond and square configurations
NEXT STEPS
  • Study the application of Faraday's Law in different geometric configurations
  • Explore the concept of magnetic flux and its dependence on shape orientation
  • Investigate the differences in induced current behavior between various loop shapes
  • Learn about the effects of velocity on induced emf in moving loops
USEFUL FOR

Physics students, educators, and anyone studying electromagnetic induction, particularly those interested in the behavior of induced currents in different geometric configurations.

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Homework Statement


Find the total maximum induced current for the diamond-shaped metal loop that is moving at a speed of 10 m/s towards a uniform magnetic field of 0.8T. All four lengths equal 10 cm or 0.01 m.
upload_2016-11-7_20-7-54.png


Homework Equations


emf = -dΦB/dt
ΦB=∫B*dA
A = (1/2)bh

The Attempt at a Solution


I need more of explanations than getting help on getting the values. I am confused on the picture above and the induced current graphs both loops show. I don't understand why the induced current graph for the diamond shape is not the same as for the square loop one. Why would the induced current decrease when half of the diamond shape metal loop is halfway in the uniform magnetic field? I know that the magnetic flux for both loops increases as they move into the uniform magnetic field, but shouldn't the induced current graph for the square loop be the same one for the diamond shape or for any square shape rotated at any degrees? Even if you get to the halfway mark on the diamond shape, the induced current should be constant and not decreasing from there. Because the area of half of that diamond shape loop is the same as a half of the square shape loop. But then, the graph doesn't show the current decreasing once the square loop is halfway into the magnetic field.
 
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When the right corner of the diamond has moved a distance x into the B-field, what is the flux through the diamond (assuming the diamond is less than halfway in)? Express the flux in terms of x and B.

Repeat for the square when it has moved a distance x into the field. Compare the two cases in terms of how the flux varies with x.
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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