# Homework Help: Loop in a B-Field

1. May 29, 2006

### choey

A circular loop with radius a = 0.25 m and N = 17 turns lies in the plane of the page (x-y plane). The wire used in constructing the loop has a resistance per unit length of dR/dl = 0.11 W/m.

A spatially uniform magnetic field points in the -z direction (into the page). In the interval between t = 0 and 15 s, the strength of this field varies according to the expression B(t) = 0.01 t^3 T/s3.

Calculate the current in the windings at t = 8 s. (Give the magnitude and algebraic sign - let a current that is clockwise in the view shown in the figure defined to be positive.)

---

First, I calculated the B-field @ t=8, which turned out to be 6.408849013 V.
Now, to find the current, I'm advised to write the equivalent Kirchoff's loop equation. I'm having a hard time doing this, because I'm given dR/dI, instead of just R. Since it's "resistance per unit length", I multiplied by 2pi*RN. What happens then?

2. May 29, 2006

### arunbg

What is the general expression for finding out induced emf wrt flux change ?
What is the value of induced emf at t = 8sec

Multiplying by 2pi*r*N would give you total resistance R.
Now you have induced emf and resistance. How will you find the current ?

Arun

3. May 29, 2006

### choey

Huh. I swear I tried that to find R and therefore I. But this time it worked, actually. :)

Now I'm asked, "In the time interval between 0 and 15 s, how much electrical charge passes any given point in the windings? (Give magnitude only.)"

I have...
emf @ t=8 : dPhi/dt = 6.408849013 V
I @ t=8 : dQ/dt = -2.181818 A
R = 2.937389131 Ohms

Q = -2.181818t, right?
So, Q(15) - Q(0) = -2.181818 * 15 = 32.72727 C, but that was too easy and wrong. Where should I be headed?

EDIT:

I also tried this:
Since I know that Phi = BA = 0.01t^3 * 2pi * 0.25^2 * 17 (the # of windings) = 0.0333794219t^3
Then I have this equation:
d(0.1963495408t^3)/dt = 2.937389131 * dQ/dt.
I integrate both sides w/ respect to t, and I get
0.1963495408t^3 = 2.937389131*Q(t)
Then Q(t) = 0.0668449198t^3
Evaluating Q(t) for t=0..15, I get
0.0668449198(15)^3 = 225.6016042 C, which is still wrong.

EDIT:

I got it :)

Last edited: May 29, 2006