How to find magnetic field in a square coil next to an RC circuit

[davidhowie34]

Homework Statement

1. (35 pts) You have a coop job helping to test a capacitor energy storage system. There is a rather large capacitor with capacitance, C = 2.02F. It is charged to a potential V = 602.V with the polarity of the capacitor as shown. The large, solid line on the right of the R–C circuit represents a conducting rod which is quite long. To the right of this rod, more or less in its center, there is a small square coil with N = 128 turns, and side a = 10 cm which is a distance b = 0.21 cm away from the rod.

a.) (5 pts) If the time constant of the circuit is to be 60.6 s, what should be the resistance of the resistor R1?

b.) (5 pts) How much energy will be stored on the capacitor?

c.) (5 pts) At t = 0, the switch S is closed. What will be the initial current I0?

d.) (8 pts) At the distance b = .21 cm, what is the magnetic field B at t = 35s?

e.) (8 pts) At t = 35s, what is the induced emf in the coil?

f.) (5 pts) Is the current in the coil clockwise or counter-clockwise? Explain why
[/B]

Homework Equations

B=mu0/2a, Emf/R=I0, V/r(e^-t/RC),[/B]

The Attempt at a Solution

a)we know that for an RC circuit, time constant is given by

tau = RC

R = tau/C

R = 60.6/2.02 = 30 Ohm

Hence, R = 30 Ohm

b)energy stored will be:

U = 1/2 C V^2

U = 1/2 x 2.02 x 602^2 = 366028.04 J

Hence, U = 366028.04 J = 3.66 x 10^5 J

c)The initial current would be:

I = V/R = 602/30 = 20.07 A

Hence, I = 20.07 A.

heres where it gets hard.

I know that the normal equation for finding magnetic field a distance away from a current source is B=u0I/2a, however, what am i to do when there is a coil at that distance? And then of course, once i figure this out, the induced emf is just the change in the flux which is BA and the direction can be found with the righthand rule. I just can't figure this one out.

 

[rude man]

A drawing would help.

 

[davidhowie34]

http://imgur.com/a/lVOSx

 

[rude man]

I know that the normal equation for finding magnetic field a distance away from a current source is B=u0I/2a

I would re-examine that belief since it's wrong.

And then of course, once i figure this out, the induced emf is just the change in the flux which is BA and the direction can be found with the righthand rule. I just can't figure this one out.

Will B be the same at all distances d from the rod, b < d < a? If not, what value(s) of B did you have in mind?

 

[davidhowie34]

I would re-examine that belief since it's wrong.Will B be the same at all distances d from the rod, b < d < a? If not, what value(s) of B did you have in mind?

okay that one is for loops.

B will be the same value throughout the entire coil I believe. I just don't understand how to get it. My friend told me to calculate the charge in the capacitor at t-35, and then find the elctric field at that point, and then convert the electric field to the magnetic field. I am not sure if this is correct. Is it?

 

[rude man]

okay that one is for loops.

B will be the same value throughout the entire coil I believe.

Why should it be? Aren't some parts of the loop closer to the rod than other parts? Doesn't that suggest that B is larger the closer you are to the rod?

My friend told me to calculate the charge in the capacitor at t=35, and then find the electric field at that point, and then convert the electric field to the magnetic field. I'm not sure if this is correct. Is it?

In a word, no. Calculate the current in the rod at t, then at t=35s, then compute B(t) at b, then flux Φ(t) in the loop, then dΦ/dt at t=35. Think integration to get B(t,r) with r the ⊥ distance from the rod to a point inside the loop.