The solutions and question make NO SENSE AT ALL

[flyingpig]

Homework Statement

A coil formed by wrapping 50 turns of wire in the shape of a square is positioned in a magnetic field so that the normal to the plane of the coil makes an angle of 30 degrees with the direction of the field. When the magnetic field is increased uniformly from 200uT to 600uT in 0.4s, an emf of magnitude 80mV is induced in the coil. What is the total length of the wire?


solution

http://img163.imageshack.us/img163/5214/73297833.th.png

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First of all the equation is wrong, shouldn't it be $$\varepsilon = -\frac{d\Phi}{dt}$$?

Secondly where did they get 4lN = length from?

 

[flyingpig]

Also you can't have "imaginary" length numbers

 

[Borek]

Secondly where did they get 4lN = length from?

Geometry? What is l, what is N?

 

[da_nang]

That's what it is. ε = -dΦ/dt, where Φ = BA*cosθ, B is magnetic field strength, A is the area. The cosine is there because you want the area perpendicular to the magnetic field. And if you have a coil with N loops, then Φ = NBA*cosθ. Since the change is uniform, delta can be used instead of d/dt.

 

[flyingpig]

Geometry? What is l, what is N?

l is the side of the square, N is the number of turns

 

[cupid.callin]

they have used ε = -dΦ/dt
here - is just for direction which you can figure out anyway ... so ignore it

now l is edge length of square ... now as "da_nang" said ... Φ = N B A cosθ

now just rearrange to get l

and perimeter = length of each square = 4l
and there are N squares so total length is 4Nl

 

[cupid.callin]

Also you can't have "imaginary" length numbers

what does that mean?

 

[flyingpig]

How can you just "get rid of it", I thought the math actually takes care of the minus sign.

 

[cupid.callin]

How can you just "get rid of it", I thought the math actually takes care of the minus sign.

- sign tells about direction
- rest about mag

so find mag by formula and direction by lenz law

no need to consider - sign ... it has no mathematical flaw

 

[Borek]

In other words - you are asked about length of the wire, doesn't matter if it is winded CW or CCW.