What is the direction of the current in the given image?

[Coderhk]

Homework Statement

In the picture 20.40, what is the direction of the current induced in the resistor at the instant the switch is closed.[/B]

Homework Equations

Right hand rules- Point thumb in direction of current and your fingers will curl in direction of magnetic field.
Lenz's law. The induced current always opposes the change in magnetic flux.

The Attempt at a Solution

When the switch is closed the current will flow counter clockwise.Which implies the left side of the solenoid is north and the right side is south. Hence the magnetic field lines go from left to right. Here I assume that the magnetic field lines generated by the solenoids intersect the resistor. If the lines go from left to right, by Lenz's law the induced current must generate a magnetic field from right to left. Using the right hand rule, I get that the result is from right to left. The answer in the book is left to right.

 

[TSny]

Describe the direction and relative magnitude of B inside the solenoid.

 

[Coderhk]

I'm guessing that the magnetic south would point to magnetic north in a straight line with a magnitude greater than the outside of the solenoid due to Ampere's law. Which could mean that the magnetic field inside the solenoid is enough to cancel out the magnetic field outside the solenoid and have extra fields pointing from south to north. This could imply that the net magnetic flux of the entire system of the solenoid is from south to north. Therefore, the current must generate a magnetic field which opposes the magnetic field inside the solenoid due to Lenz's law hence from north to south. Is this insight correct?

I was also wondering when using the rule that :"point your thumb in the direction of the magnetic field and your fingers will curl in the direction of the magnetic field" wouldn't the magnetic field generated at the top of the wire cancel out the magnetic field on the bottom?

 

[TSny]

I'm guessing that the magnetic south would point to magnetic north in a straight line with a magnitude greater than the outside of the solenoid due to Ampere's law. Which could mean that the magnetic field inside the solenoid is enough to cancel out the magnetic field outside the solenoid and have extra fields pointing from south to north. This could imply that the net magnetic flux of the entire system of the solenoid is from south to north. Therefore, the current must generate a magnetic field which opposes the magnetic field inside the solenoid due to Lenz's law hence from north to south. Is this insight correct?

Yes, very good.

I was also wondering when using the rule that :"point your thumb in the direction of the magnetic field and your fingers will curl in the direction of the magnetic field"

Did you mean, "point your thumb in the direction of the current"?

wouldn't the magnetic field generated at the top of the wire cancel out the magnetic field on the bottom?

I'm not quite following you here. Which "wire" are you referring to?

 

[Coderhk]

Yes, I meant "point your thumb in the direction of the current"? In the picture I uploaded, the arrows are pointing in opposite direction. Hence wouldn't net two sides cancel each other out giving a net magnetic flux of zero?

 

[Coderhk]

Yes, very good.

How do I position my hand such that the magnetic field is pointing from north to south? Do I use this right hand rule "Point thumb in direction of current and fingers curl in direction of magnetic field?"

 

[TSny]

Yes, I meant "point your thumb in the direction of the current"? In the picture I uploaded, the arrows are pointing in opposite direction. Hence wouldn't net two sides cancel each other out giving a net magnetic flux of zero?

I'm still not sure what you are asking about. (I can be very dense at times!) I'm a little lost as to what the "two sides" refer to, and I'm not sure at what particular point of space you think the B field of the two sides should cancel. Are you considering a loop of current and wondering why the B field doesn't cancel out at the center of the loop?

How do I position my hand such that the magnetic field is pointing from north to south?

Inside the solenoid, the B field points from the south pole towards the north pole.
http://www.excelatphysics.com/magnetic-field-pattern.html

Do I use this right hand rule "Point thumb in direction of current and fingers curl in direction of magnetic field?"

Yes, you can use that rule.

See the above link. Also look here to see some applications of the rule: http://philschatz.com/physics-book/contents/m42382.html
If you scroll down at this link, you will see the right hand rule applied to a current loop and then a solenoid. Does this help?

 

[Coderhk]

I'm still not sure what you are asking about. (I can be very dense at times!) I'm a little lost as to what the "two sides" refer to, and I'm not sure at what particular point of space you think the B field of the two sides should cancel. Are you considering a loop of current and wondering why the B field doesn't cancel out at the center of the loop?

In the picture I uploaded below, ignoring the content of the picture except for the hand, in one pic the guy curled his fingers a little and his fingers point left, however in the second pic when he curls his finger more the magnetic field points right. Lastly in the third, the magnetic field is pointing left when his fingers are behind the wire and right when the fingers are in front of the wire.

 

[Coderhk]

In this pic the part of the pic which is circled in white is pointing left however the fingers in the red circle are pointing right. Why don't those two part cancel each other out?

 

[TSny]

In the figure below points $a$ and $b$ are on opposite sides of the wire. The magnetic field at point $a$ is in the opposite direction of the magnetic field at point $b$. But these fields don't cancel each other, because they are not at the same point in space.

 

[Coderhk]

In the figure below points $a$ and $b$ are on opposite sides of the wire. The magnetic field at point $a$ is in the opposite direction of the magnetic field at point $b$. But these fields don't cancel each other, because they are not at the same point in space.
View attachment 220669

However would the net magnetic flux of the entire system be 0?

 

[TSny]

However would the net magnetic flux of the entire system be 0?

I'm sorry. I don't understand what is meant by "the net magnetic flux of the entire system".
Magnetic flux $\Phi$ involves both the magnetic field and some surface area. I'm not sure what surface area you are thinking about.

 

[Coderhk]

I still am not sure how I am suppose to solve the original problem. Regardless of what way the current flow in the resistor it can't oppose the B of the solenoid. I drew a picture of my interpretation of the situation.

 

[Coderhk]

I'm sorry. I don't understand what is meant by "the net magnetic flux of the entire system".
Magnetic flux $\Phi$ involves both the magnetic field and some surface area. I'm not sure what surface area you are thinking about.

I mean the magnetic flux of the square in the picture you uploaded.

 

[TSny]

Suppose we look at your setup from the viewpoint of looking straight into one end of the solenoid: The gray area is the solenoid cross-section.

The outer circular loop contains the resistor R. Suppose that when the switch is closed in the solenoid circuit, the magnetic field inside the solenoid increases in strength and points out of the page (as shown by the dots inside the solenoid). You don't need to worry about the magnetic field outside the solenoid since it's the field inside that produces the major part of the flux through the resistor circuit.

What would be the direction of the induced current in the resistor circuit?

 

[Coderhk]

If it was to flow from left to right the induced current would produce a magnetic field that would look like this :

However the part outside of the circle is helping the magnetic field. Where as if it was to flow from right to left the "X" and "dots" would be flipped. In both situations part of it is helping the solenoid's magnetic field. I'm guessing it would flow left to right since the opposing field is closer to the solenoid. May I conclude that when deciding the direction, I just find the direction such that the opposing field is closer to the source. If it went from right to left the opposing field would be further(outside of the circle) from the source hence it does less opposing.

 

[TSny]

From Faraday's law, the induced emf in the resistor circuit depends only on the change in magnetic flux through the resistor circuit. That is, you only need to concentrate on the yellow area in the diagram below. Any magnetic field outside the yellow area is irrelevant.

 

[Coderhk]

I think I get it. I greatly appreciate your time and effort explaining it. Thank you very much. :D

 

[TSny]

Very good. Glad it makes sense now.