AP Physics E&M MC: Electric Field, Induction, LC Circuit

In summary, the conversation discusses several problems involving electric potential, magnetic fields, and LC circuits. The solution to problem 18 is B, as the strength of the electric field is the change in voltage over the change in distance. For the Lenz' law problem, the direction of flux is into the ring and the current is clockwise, as it opposes the change in magnetic field from the wire. The solution to problem 35 involves deriving the angular frequency of an LC oscillator, which can be found by plugging in an equation for the charge of the capacitor and solving the ODE for voltage. The final result is ω=1/\sqrt{LC} where L and C are the inductance and capacitance of the circuit,
  • #1
pietastesgood
30
0

Homework Statement




Answer is B.

Answer is E.

Answer is E.

Homework Equations



E=F/q
E=V/d
Right hand rule for inductors

The Attempt at a Solution



Quite confused for these problems. For number 18, I'm quite baffled as to where the 0.04 meters even comes from. What I had attempted to do was find the potential at the point, 25 V, and divide it by the radius, or √(.15^2+.08^2), but that didn't even yield one of the answers. Then I realized that the potential was actually increasing as x increased, and that the object causing the electric field was likely off the graph. Then I just got really confused.

For number 33, I thought it was C. As the switch is flipped, there is a sudden increase in current in the top loop. This current flows out of the positive terminal, through the resistor, and back to the negative terminal. Since the current flows from left to right near the wire loop, the magnetic field generated should be into the page, right? Thus, to counteract this, a current that is counterclockwise will be generated in the loop. Unless I did the right hand rule wrong, that's what it should be. But the answer is E.

For number 35, I don't really understand what the question is asking. I've never learned about the frequency and oscillating of the current in a circuit, with just a LC circuit. Utterly confused here.

Would greatly appreciate any help! Thanks in advance!
 
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  • #2
Too many problems for one go!

For the ring problem: what is the direction of discharge current? So then what is the direction of the magnetic flux through the ring? Then either go with Lenz' law or Faraday's law to determine the direction of ring current. Lenz' is easier).

Is the discharge current increasing or decreasing with time?
 
  • #3
pietastesgood said:

Homework Statement



[ IMG]http://imageshack.us/a/img405/2379/182008.jpg[/QUOTE]
attachment.php?attachmentid=58646&stc=1&d=1368293443.jpg

Answer is B.

[ IMG]http://imageshack.us/a/img526/5937/332008.jpg
Answer is E.
[ IMG]http://imageshack.us/a/img203/9984/352008.jpg
Answer is E.

Homework Equations



E=F/q
E=V/d

The Attempt at a Solution



Quite confused for these problems. For number 18, I'm quite baffled as to where the 0.04 meters even comes from. What I had attempted to do was find the potential at the point, 25 V, and divide it by the radius, or √(.15^2+.08^2), but that didn't even yield one of the answers. Then I realized that the potential was actually increasing as x increased, and that the object causing the electric field was likely off the graph. Then I just got really confused.
...

Would greatly appreciate any help! Thanks in advance!

It's best not to put too many questions into one thread.

What radius are you referring to ?
How far are the 30V and 20V equi-potential lines apart in the vicinity of point P ?
 

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  • #4
pietastesgood said:
...

For number 35, I don't really understand what the question is asking. I've never learned about the frequency and oscillating of the current in a circuit, with just a LC circuit. Utterly confused here.

Would greatly appreciate any help! Thanks in advance!
What did you learn regarding LC circuits ?
 
  • #5
Oops, I'll make sure to spread the problems apart more next time. I understand number 18 now. E=-dV/dr, so the strength of the electric field is the change in voltage/change in distance. So since the equipotential lines for 20 and 30 V are .04 m apart, it would be a change of 10 V/a change of .04 m, so B.

For the Lenz' law problem, the direction of discharge out the positive terminal and along the right on the bottom of the circuit. Direction of magnetic flux is downward through the ring. Ring will attempt to counteract that, so it creates magnetic flux upward. According the to RHR, that makes the current counterclockwise, which makes me confused since the answer is clockwise. Did I have a logical error somewhere? Discharge current decreases over time.

Regarding LC circuits, I only learned that at t=0, an inductor in a circuit acts like a broken wire, while at t=∞ it acts like a wire.
 
  • #6
pietastesgood said:
For the Lenz' law problem, the direction of discharge out the positive terminal and along the right on the bottom of the circuit. Direction of magnetic flux is downward through the ring.
Direction of flux is INTO the ring (into the page).
Ring will attempt to counteract that, so it creates magnetic flux upward. According the to RHR, that makes the current counterclockwise, which makes me confused since the answer is clockwise. Did I have a logical error somewhere? Discharge current decreases over time.
EDIT: Nope, I'm wrong. Stay tuned for an explanation.
 
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  • #7
Assume for the moment the B field due to the wire is increasing. That would generate a B field in the ring to oppose the buildup of total B in the ring, so that current would be ccw. But the wire current is decreasing, so the ring current will be cw to try to maintain the total ring B field unchanged. In other words, the ring current opposes the direction of change of wire B, which is negative, not B itself. So the answer is indeed E.
 
  • #8
Aha! That makes sense. Thank you! Now, just the oscillator problem.
 
  • #9
pietastesgood said:
Aha! That makes sense. Thank you! Now, just the oscillator problem.

OK, if you don't know the formula for the oscillating frequency of an L-C oscillator you'll have to derive it!

Connect a C and an L together, put an initial charge on C and solve the ODE for V(t)!
 
  • #10
I got some of it after looking up a video on Youtube.

ε=Q/C for a capacitor

Q/C - L(dI/dt) = 0
Q/C - L(-d[itex]^{2}[/itex]q/dt[itex]^{2}[/itex]) = 0
d[itex]^{2}[/itex]q/dt[itex]^{2}[/itex] = -Q/LC

However, I don't quite follow how the angular frequency ω=1/[itex]\sqrt{LC}[/itex] from that second ODE.
 
  • #11
pietastesgood said:
I got some of it after looking up a video on Youtube.

ε=Q/C for a capacitor

Q/C - L(dI/dt) = 0
Q/C - L(-d[itex]^{2}[/itex]q/dt[itex]^{2}[/itex]) = 0
d[itex]^{2}[/itex]q/dt[itex]^{2}[/itex] = -Q/LC

However, I don't quite follow how the angular frequency ω=1/[itex]\sqrt{LC}[/itex] from that second ODE.

Stick q = q0*cos[t/√(LC)] into your last equation, what do you get?
(q0 is the initial charge on C).
 
  • #12
d^2q/dt^2 = -q0*cos[t/√(LC)]/LC

I'm only in Calculus II, so I don't really follow how to solve the second order differential equation.
 
  • #13
pietastesgood said:
d^2q/dt^2 = -q0*cos[t/√(LC)]/LC

I'm only in Calculus II, so I don't really follow how to solve the second order differential equation.

Pleae look at post #11 again. You don't have to solve it. I made the assumption that you didn't know how.
 
  • #14
Sorry, but I'm not sure what else I can do with plugging in q = q0*cos[t/√(LC)] into the second order differential equation, other than replacing -Q/LC with -q0*cos[t/√(LC)]/LC.
 
  • #15
pietastesgood said:
Sorry, but I'm not sure what else I can do with plugging in q = q0*cos[t/√(LC)] into the second order differential equation, other than replacing -Q/LC with -q0*cos[t/√(LC)]/LC.

First of all, there is only one q. Don't call it q one time and Q another.

If q = q0*cos[t/√(LC)] what is d2q/dt2?

Now, put that into your equation. What do you get? An identity, perhaps?
 
  • #16
Well, taking the second derivative of q0*cos[t/√(LC)] yields -(q0/(LC))*cos(t/√(LC))

Setting that equal to -q/LC, simplifying, I get q0cos(t/√(LC))=q again. Pretty sure I didn't reach the right conclusion there.
 
  • #17
pietastesgood said:
Well, taking the second derivative of q0*cos[t/√(LC)] yields -(q0/(LC))*cos(t/√(LC))

Setting that equal to -q/LC, simplifying, I get q0cos(t/√(LC))=q again. Pretty sure I didn't reach the right conclusion there.
Yes. You got an identity which means the solution for q that I gave you is a correct solution.

Now, if someone gives you a signal cos(t/√(LC) do you think you can figure out what the frequency of that signal is?
 
  • #18
Oh, right. cos(wt)=cos(t/√(LC)), so w=1/√(LC)
There we go!
 

1. What is an electric field?

An electric field is a physical field that surrounds and exerts a force on any object with an electric charge. It is created by electrically charged particles and can be either positive or negative. The strength and direction of the electric field is determined by the magnitude and location of the charges.

2. How is electric field strength calculated?

Electric field strength is calculated by dividing the force exerted on a point charge by the magnitude of the charge. It is represented by the equation E = F/q, where E is the electric field strength, F is the force, and q is the charge.

3. What is electromagnetic induction?

Electromagnetic induction is the process of generating an electric current in a conductor by varying the magnetic field around it. This can be achieved by moving the conductor through a magnetic field or by changing the magnetic field around the conductor.

4. What is a LC circuit?

A LC circuit is a type of electrical circuit consisting of an inductor and a capacitor connected in series or parallel. The inductor stores energy in the form of a magnetic field, while the capacitor stores energy in the form of an electric field. When connected, the circuit can oscillate at a specific frequency, known as the resonant frequency.

5. How is the resonant frequency of a LC circuit calculated?

The resonant frequency of a LC circuit is calculated by the equation f = 1/(2π√(LC)), where f is the resonant frequency, L is the inductance, and C is the capacitance. This frequency is also known as the natural frequency of the circuit and is dependent on the values of the inductor and capacitor.

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