Question

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)

Answer 1

@ganeshie8 @Miracrown @iambatman @dan815

Answer 2

This 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

Answer 3

While the correct answer is "zero"

Can anyone help me with this?

Answer 4

Sorry, 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?

Answer 5

Ohk! Take your time buddy.

Answer 6

What I'm thinking is, we have to calculate current through AB.... so, that should make a difference, will it? @dan815

Answer 7

Yeah... and perpendicular to area vector is parallel to B vector.. ain't it?

Answer 8

Ouch! :P

The diameter has no surface, that's why..?

Answer 9

Oh, so, even if it was for the whole circular loop, the answer would have been zero..?

Answer 10

starting over lol

Answer 11

uhmm...? :/ confused

Answer 12

okay 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

Answer 13

@Jhannybean

Answer 14

It simply means - \(\cfrac{dB}{dt} = - \alpha \)

Now if you differentiate it again, it will give you "zero" ... So, it is decreasing constantly !

Answer 15

Ignore that "-" before dB/dt

Answer 16

are u sure, the way the wrote it can be interpreted both ways

Answer 17

"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