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mathslover
 one year ago
The radius of the circular conducting loop is R. Magnetic Field is decreasing at a constant rate \(\alpha\) (inwards to the plane of loop). Resistance per unit length of the loop is \(\rho\). The current in wire AB is? (AB is one of the diameters)
mathslover
 one year ago
The radius of the circular conducting loop is R. Magnetic Field is decreasing at a constant rate \(\alpha\) (inwards to the plane of loop). Resistance per unit length of the loop is \(\rho\). The current in wire AB is? (AB is one of the diameters)

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mathslover
 one year ago
Best ResponseYou've already chosen the best response.1@ganeshie8 @Miracrown @iambatman @dan815

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1This is what I've tried : \(i = \cfrac{1}{r} \cfrac{d\phi}{dt} = \cfrac{1}{r} \cfrac{S dB}{dt} \) where \(\phi\) is magnetic flux. \(r\) is resistance. \(S\) is the area A of the circular loop. I've been given with : \(\cfrac{r}{2 \pi l } = \rho \implies r = \rho \times 2 \pi l= \rho \times 2 \pi (2R)\) and \(S = \pi (R^2)\) So, we have : \( i = \cfrac{1}{\rho \times 4 \pi R} \times \pi (R^2) \times ( \alpha) \) \(i = \cfrac{R \alpha}{4 \rho } \) And direction of current will be from B to A dw:1433312077316:dw

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1While the correct answer is "zero" Can anyone help me with this?

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Sorry, didn't get you. We have \(\phi = \bf{B} . \bf{S} \) Right? And the angle between S and B is 0 degrees. So, why would it be zero?

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Ohk! Take your time buddy.

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1What I'm thinking is, we have to calculate current through AB.... so, that should make a difference, will it? @dan815

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Yeah... and perpendicular to area vector is parallel to B vector.. ain't it?

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Ouch! :P The diameter has no surface, that's why..?

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Oh, so, even if it was for the whole circular loop, the answer would have been zero..?

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1uhmm...? :/ confused

dan815
 one year ago
Best ResponseYou've already chosen the best response.3okay so, let me see if i got this question right, does it mean mag field is increasing over time, or its decreasing constnatly spatially as u get closed to the center

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1It simply means  \(\cfrac{dB}{dt} =  \alpha \) Now if you differentiate it again, it will give you "zero" ... So, it is decreasing constantly !

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Ignore that "" before dB/dt

dan815
 one year ago
Best ResponseYou've already chosen the best response.3are u sure, the way the wrote it can be interpreted both ways

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1"According to the Lenz's law emf's of the same magnitude in the clockwise direction are induced in the two loops into which the figure is divided. So, current is induced in the clockwise direction in the outer boundary but no current in wire AB" This is what I got when I searched (just now) on google... https://books.google.co.in/books?id=zlWRMWEcJG0C&pg=PA349&lpg=PA349&dq=The+radius+of+the+circular+conducting+loop+is+R.+Magnetic+Field+is+decreasing+at+a+constant+rate&source=bl&ots=saTfbsAdfw&sig=cETI6m4U9WxnEfIW1hiHEJlQLJU&hl=en&sa=X&ei=U6FuVeq0CtGUuATVmIKwBQ&ved=0CB4Q6AEwAA#v=onepage&q=The%20radius%20of%20the%20circular%20conducting%20loop%20is%20R.%20Magnetic%20Field%20is%20decreasing%20at%20a%20constant%20rate&f=false

dan815
 one year ago
Best ResponseYou've already chosen the best response.3yah there is a current induced in the outerloop

dan815
 one year ago
Best ResponseYou've already chosen the best response.3but in the center wire i think the current tries to flow both ways and cancels out u have no flow

dan815
 one year ago
Best ResponseYou've already chosen the best response.3it always wants ot go in counter clockwise or clockwise whatever result u got for the outerloop

dan815
 one year ago
Best ResponseYou've already chosen the best response.3but if the top part wants to go clockwise and bottom loop too , and the total current is equal everywhere

dan815
 one year ago
Best ResponseYou've already chosen the best response.3there u must have no flow in the middle

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Oh WOW! Excellent. Thanks a lot Dan! :)

dan815
 one year ago
Best ResponseYou've already chosen the best response.3make sure u understand why this argument works only for electromagnetic induced currents

dan815
 one year ago
Best ResponseYou've already chosen the best response.3normally this wont happen in a circuit

dan815
 one year ago
Best ResponseYou've already chosen the best response.3but since its EMF induced they wanna maintain that clockwise or ccw flow

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, I understand that point. Thanks again! :)

dan815
 one year ago
Best ResponseYou've already chosen the best response.3ok also u can show it mathematically

dan815
 one year ago
Best ResponseYou've already chosen the best response.3if u calculate the 2 semicircle loops separetely

dan815
 one year ago
Best ResponseYou've already chosen the best response.3u can solve for each semi circle given that B field

dan815
 one year ago
Best ResponseYou've already chosen the best response.3and ull end up with zero again

dan815
 one year ago
Best ResponseYou've already chosen the best response.3cuz again ull get the current flow in opposite directions, which is more rigorous

mathslover
 one year ago
Best ResponseYou've already chosen the best response.1I see! Thanks for making it clear to me from every angle. :) Mr. Lifesaver :D
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