Passage V (question 29) TBR electrostatic/magnetism chapter

[orangetea]

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Background info:
Loop C is rectangular with edges 6 cm and 8 cm
Loop E is circular with radius 4 cm

Question 29 asks which graph accurately reflects the current associated with the Loop E

So between these two graphs I picked the rectangular looking one(sorry for the horrible drawing, assume that the half circle/half squares are symmetrical and x axis= time y axis= current)


here is the answer explanation: We must determine whether the current is constant or varies as the loop enters and exists the field. as with the circular loop. unlike the rectangular loop, the area of the loop entering the field and thus the magnetic flux changes as the loop enters the field. As the circular loop enters the field the magnetic flux increases at an increasing rate until the loop is half way in, after which the magnetic flux increases at a decreasing rate. This is best described(in the half circle looking graph).

It also says that the square looking graph cannot be correct because the magnetic flux does not increase at a uniform rate, so current cannot flow at a constant rate during induction periods.


My questions:
1. Would the rectangular looking graph be correct for the rectangular loop?
2. How is flux not increasing uniformly when it depends on the change in magnetic field over time? and the magnetic field is constant.

 

[HelpMeOutPlease1]

The Rectangular box is incorrect, because it is implying that as soon as you put a tiny part of the ring into the field, that it will cause it to have the same induced current as when half of the ring has entered.

Think of this like slowly inserting a ring into the field. The more you insert the stronger the induced current, up until you reach the halfway point. Because the middle point of the ring is the maximum amount of "new" ring added. After the halfway point, you can add progressively less to the field, therefore decreasing the induced current.
I think that's right.

I just had a question as how it is possible to have a "negative" induced current?

 

[BerkReviewTeach]

My questions:
1. Would the rectangular looking graph be correct for the rectangular loop?
2. How is flux not increasing uniformly when it depends on the change in magnetic field over time? and the magnetic field is constant.
View attachment 183050

1) A rectangular loop at uniform speed would enter the field in such a way that the flux (magnetic field within the loop) would increase at a constant rate, so the emf would be constant. This results in a current of constant magnitude (like your second picture above). The equal but opposite effect would be observed exiting the field. So yes, a rectangular loop gives a graph that looks like rectangles (although the dimensions of the graph depend on the loop speed, so they are not the exact same shape).

2) For the rectangle, the flux is increasing at a constant rate, because area entering the B field is changing at a constant rate and the B field is static. For the circle, the flux is increasing at a changing rate, because area entering the B field is changing at a constant rate and the B field is static. HMOP1 explained this quite well.

I just had a question as how it is possible to have a "negative" induced current?

Strictly an issue of sign convention for direction. As drawn in the OP's question, upon entering the field the current is clockwise, but upon exiting the field it is counterclockwise.