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Directions and EMF

  • #1

Homework Statement


An infinite straight wire carries a current I that varies with time as shown above. It increases from 0 at t = 0 to a maximum value I1 = 3.7 A at t = t1 = 14 s, remains constant at this value until t = t2 when it decreases linearly to a value I4 = -3.7 A at t = t4 = 30 s, passing through zero at t = t3 = 24.5 s. A conducting loop with sides W = 30 cm and L = 61 cm is fixed in the x-y plane at a distance d = 46 cm from the wire as shown.

What is ε1, the induced emf in the loop at time t = 7 s? Define the emf to be positive if the induced current in the loop is clockwise and negative if the current is counter-clockwise.

Image: http://img713.imageshack.us/img713/7218/h17bfromwire.png [Broken]

Homework Equations


See Below


The Attempt at a Solution



My question on the problem concerns the direction of the induced EMF. The key says it should be negative and thus a current going counterclockwise. I'm a bit confused by this. At time t= 7s, the flux is increasing because the current is increasing. Therefore, by Lenz' law, wouldn't there be an induced magnetic field into the page to offset this positive change in flux. If so, by the right hand rule, doesn't this mean that the current must flow clockwise in the loop. That's my rationale, I can't see where I'm going wrong.
 
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Answers and Replies

  • #2
The flux of the wire is increasing downwards through the loop. That is according to the right-hand rule it is coming from the top downwards through the loop. This means that the magnetic field of the loop need to be directed upwards to decrease the flux so that the current in it will be counterclockwise.
 

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