Why Doesn't Right Hand Rule #2 Work for This Capacitor's Electric Field?

In summary, if the magnetic field is decreasing in time, the induced magnetic field must be out of the page to counteract the decreasing flux according to Lenz's law. The direction of the induced current can be determined using the right hand rule, where the thumb represents the direction of the linear current and the curled fingers represent the direction of the magnetic field. Thus, the direction of the electric field between the plates of the parallel plate capacitor shown in the drawing will be determined by the direction of the induced current. The right hand rule can be used to determine this direction, taking into account the linearity of the current and the circular nature of the magnetic field.
  • #1
michaelw
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Indicate the direction of the electric field between the plates of the parallel plate capacitor shown in the drawing if the magnetic field is decreasing in time. Give your reasoning

if the magnetic field is decreasing, so is the flux, so mr. lenz says the induced magnetic field must be out of the page to counteract the decreasing flux

but with right hand rule #2, it completely depends where you put your hand in determining the direction of current

if you put it at the top of the the wire, curl fingers out of page, current goes to the right (right hand, conventional current).. ie) clockwise

if you put it at the bottom, current still goes to the right, but now it means the direction is counter clockwise.

which is right and why?? :confused: :confused:
 

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  • #2
michaelw said:
Indicate the direction of the electric field between the plates of the parallel plate capacitor shown in the drawing if the magnetic field is decreasing in time. Give your reasoning

if the magnetic field is decreasing, so is the flux, so mr. lenz says the induced magnetic field must be out of the page to counteract the decreasing flux

but with right hand rule #2, it completely depends where you put your hand in determining the direction of current

if you put it at the top of the the wire, curl fingers out of page, current goes to the right (right hand, conventional current).. ie) clockwise

if you put it at the bottom, current still goes to the right, but now it means the direction is counter clockwise.

which is right and why?? :confused: :confused:

Eh?

I'm confused too... but not with the right hand rule, but rather what you described. What do "put it at the top of the wire" and "put it at the bottom" mean?

Since the B field is decreasing, Lenz's law, as you have correctly stated, will try to preserve the original B field, and thus, will induce a current in the LOOP in the same direction as the original B field. Thus, it will produce an induced B field pointing OUT of the page. So far, we have that in agreement.

Now, use your right hand, and point your thumb in that direction. The way the rest of your fingers curl is the direction of the induced current. PERIOD.

So the current in your circuit will flow in THAT direction, causing a build-up of charge in the capacitor. I have no idea what the "top of wire" or "bottom of wire" refers to...

Zz.
 
  • #3
suppose that the circles on this page each represent my hand, with my fingers curled out of the page, and thumb pointing in direction of current (that is, to the right)

if my hand were at circle #1 (top), then current is clockwise
if my hand were at circle #2 (bottom), current is counter clockwise

the direction of current as indicated by the right hand rule is to the right. however, depending on where your hand is, that current is either going clockwise or counterclockwise

im terribly stumped and exam is tomorrow :confused:
 

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  • #4
michaelw said:
suppose that the circles on this page each represent my hand, with my fingers curled out of the page, and thumb pointing in direction of current (that is, to the right)

if my hand were at circle #1, then current is clockwise
if my hand were at circle #2, current is counter clockwise

the direction of current as indicated by the right hand rule is to the right. however, depending on where your hand is, that current is either going clockwise or counterclockwise

im terribly stumped and exam is tomorrow :confused:

No, you are applying the rule in an incorrect fashion. Your THUMB, in this case, points in the direction of the magnetic field, not your curled fingers. Why? It is because the magnetic field is "LINEAR", and has a straight line geometry. It is the CURRENT that is "curling".

For example, look at the current moving in a circular loop. How do you determine what direction the B field is? You curl your FINGERS in the direction that the current is moving, and then how your thumb points is the direction of the B field.

Now look at another situation. What if you have a straight wire with a current? Here, the current now is the one with a LINEAR geometry, i.e. moving in a straight line. In this case, the THUMB now represents the current (thumb=straight). The magnetic field is the one curling around the wire. So your curled fingers respresents the direction of the magnetic field.

Moral of the story: use your thumb to represent the "thing" that's moving in a straight line.

Zz.
 
  • #5
oops it appears I've goofed :)
i was mixing up thumb/fingers (And it looks like you replied already =)

thanks for the tip about the linearity
youre a savior

thanks again!
 

Related to Why Doesn't Right Hand Rule #2 Work for This Capacitor's Electric Field?

1. Why doesn't Right Hand Rule #2 work?

The Right Hand Rule #2 states that when a current-carrying wire is placed in a magnetic field, the direction of the force on the wire can be determined by pointing the thumb of the right hand in the direction of the current, the fingers in the direction of the magnetic field, and the palm in the direction of the force. However, in some cases, this rule may not work.

2. What are the limitations of Right Hand Rule #2?

Right Hand Rule #2 is based on the assumption that the current is moving in a straight line. If the current is not moving in a straight line, this rule will not work. Additionally, this rule only works for a single current in a magnetic field. If there are multiple currents or magnetic fields present, the rule becomes more complex and may not work as expected.

3. Can you provide an example where Right Hand Rule #2 does not work?

One example where Right Hand Rule #2 does not work is when the current is entering or leaving a magnetic field at an angle. In this case, the direction of the force may not align with the direction of the current and the magnetic field, making the rule ineffective.

4. How can I determine the direction of the force on a wire when Right Hand Rule #2 doesn't work?

If Right Hand Rule #2 doesn't work, you can use the formula F = I x B x sinθ to determine the direction of the force. This formula takes into account the angle between the current and the magnetic field and can be used for more complex situations where the Right Hand Rule #2 may not apply.

5. Are there any alternative rules to determine the direction of the force when Right Hand Rule #2 doesn't work?

Yes, there are alternative rules such as the Left Hand Rule and the Corkscrew Rule that can be used to determine the direction of the force in situations where Right Hand Rule #2 may not apply. These rules involve using the left hand, or imagining a corkscrew motion, to determine the direction of the force on a current-carrying wire in a magnetic field.

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