So I just had an exam and I'm so unsure about this problem. It seems that I got it right, but I could be completely wrong. XD(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A long, straight current-carrying wire carries an increasing current I that is uniformly distributed over the cross-section of the wire (the current density j is uniform). The magnitude of the induced electric field inside the wire is (r is the distance to the center of the wire):

a) zero at all points inside wire

b) proportional to r

c) proportional to r^2

d) proportional to 1/r

e) proportional to 1/r^2

2. Relevant equations

closed-line integral ∫B*dl = µ0 *I (enclosed)

j = I/A

closed line integral ∫E*dl = -d/dt (magnetic flux)

magnetic flux = ∫B*dA

3. The attempt at a solution

So basically I thought, since there is a current changing in time, there is a magnetic field being induced. This magnetic field, since it is proportional to the current, also changes in time, so it creates an electric field. So I began with:

∫B*dl = µ0 *I (enclosed)

The line integral was a distance r from the center where r is less than the radius of the exterior of the wire.

The I enclosed wasn't the entire I, but the ratio between the enclosed current and net current.

j = I(enclosed) /A = I(enclosed)/pir^2

I(net)/piR^2 = I(enclosed)/pir^2

r^2/R^2 * I(net) = I(enclosed)

Then substituting back into the line integral:

∫B*dl = µ0 *r^2/R^2 *I(net)

B*2pir = µ0 *r^2/R^2 *I(net)

B =1/2pi * ( µ0 *r/R^2 *I(net))

Then calculated magnetic flux:

∫B*dA =

And here is where it gets kind of fuzzy. XD I think I might have assumed that the flux was in the area of pir^2 within the wire and the B field going in the same direction as the wire. But I think the B field is actually circling that area of pir^2, so I think I made a mistake there. :\

I ended up with magnitude of E = rµ0* I/(4piR^2) and chose B. Was I completely wrong? XD

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# Current carrying wire and induced electric field within the wire

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