What is the Magnetic Field and Flux at Point O?

[Helly123]

Homework Statement

[/B]
There is lead XY shaped as straight wire. Next to it, circular lead with radius 0.10 m.
They are in the same plane.
XY to center of circle, O is 0.20 m.
Curent flowing through XY is 15.7 A

Homework Equations

The Attempt at a Solution

1) find magnetic field (B) at O[/B]
B induced by XY at O $u_0$I/2$\pi$r
B induced by Circle at O $u_0$I/2R
So i just add both?
Since B induced at O by XY is opposed direction, the current at Circular wire is opposed direction to current XY?

2) flux at O
flux = BA cos $\theta$
So A is 1? Because it just a point at O?
While, B equal to B at number 1) ?

3) when B at O set to 0 by a current passing in circular lead. Find magnitude and direction of this current
B at O is zero
This current does it refer to current at circular wire?

 

[Doc Al]

Could you please restate the problem exactly as given? Looks to me that you have current going through the straight wire and a circular area defined. Are you supposed to find the flux through that area?

 

[Helly123]

Could you please restate the problem exactly as given? Looks to me that you have current going through the straight wire and a circular area defined. Are you supposed to find the flux through that area?

This is it. Hope it shows clear

It only says that, flux at O.

 

[Doc Al]

OK, much clearer. For parts 1 & 2 you only need consider the magnetic field generated by the straight wire.

 

[Helly123]

OK, much clearer. For parts 1 & 2 you only need consider the magnetic field generated by the straight wire.

For 1) the formula before is correct?
For 2) i simply count Area as 1?

 

[Doc Al]

Ah, it looks like they are distinguishing B (magnetic flux density) from H (magnetic field strength). For this problem, they are simply related. See: Magnetic Field

(I'm too used to calling B the magnetic field strength, as done in most elementary books.)

 

[Helly123]

Ah, it looks like they are distinguishing B (magnetic flux density) from H (magnetic field strength). For this problem, they are simply related. See: Magnetic Field

(I'm too used to calling B the magnetic field strength, as done in most elementary books.)

For number 1) i have to find H = 1.25 A/m
For number 2) i have to find B = 1.57 10^-6 Wb/m^2

As for number 3.
1.25 A/m
How many meter to be counted for that circular wire? How to tell that the induced current have opposite direction to current XY?

 

[Doc Al]

How many meter to be counted for that circular wire?

You need to know how to find the field at the center of a current loop.

How to tell that the induced current have opposite direction to current XY?

You'd use a version of the right-hand rule. For example, a clockwise current in that circular loop would produce a field (at the center) going into the page.

You know the direction of the field from the straight wire (from another version of the right-hand rule) so the field from the current loop must oppose that direction to cancel it.

 

[Helly123]

You need to know how to find the field at the center of a current loop.You'd use a version of the right-hand rule. For example, a clockwise current in that circular loop would produce a field (at the center) going into the page.

You know the direction of the field from the straight wire (from another version of the right-hand rule) so the field from the current loop must oppose that direction to cancel it.

Ok.
The induced current always opposed to the original?
Btw. When i calculated H
the formula is H = B/$u_o$ - M
What is M? M for the lead?

 

[Doc Al]

The induced current always opposed to the original?

There's no induced current here. (The magnetic field is not changing.) There is the field from the straight wire and the field from the circular loop. They must oppose each other since you are asked for the current in the loop that gives zero net field in the center.

Ok.
Btw. When i calculated H
the formula is H = B/$u_o$ - M
What is M? M for the lead?

I'm assuming this is a loop of wire with nothing inside it. So all you need is H = B/$u_o$.

 

[Helly123]

There's no induced current here. (The magnetic field is not changing.) There is the field from the straight wire and the field from the circular loop. They must oppose each other since you are asked for the current in the loop that gives zero net field in the center.I'm assuming this is a loop of wire with nothing inside it. So all you need is H = B/$u_o$.

Do you have article about loop wire next to straight wire?

 

[Helly123]

There's no induced current here. (The magnetic field is not changing.) There is the field from the straight wire and the field from the circular loop. They must oppose each other since you are asked for the current in the loop that gives zero net field in the center.I'm assuming this is a loop of wire with nothing inside it. So all you need is H = B/$u_o$.

How come there is magnetic field from loop if there is no current induced in it?

 

[jishnu]

Homework Statement

View attachment 224974 [/B]
There is lead XY shaped as straight wire. Next to it, circular lead with radius 0.10 m.
They are in the same plane.
XY to center of circle, O is 0.20 m.
Curent flowing through XY is 15.7 A

Homework Equations

The Attempt at a Solution

1) find magnetic field (B) at O[/B]
B induced by XY at O $u_0$I/2$\pi$r
B induced by Circle at O $u_0$I/2R
So i just add both?
Since B induced at O by XY is opposed direction, the current at Circular wire is opposed direction to current XY?

2) flux at O
flux = BA cos $\theta$
So A is 1? Because it just a point at O?
While, B equal to B at number 1) ?

3) when B at O set to 0 by a current passing in circular lead. Find magnitude and direction of this current
B at O is zero
This current does it refer to current at circular wire?

I have a doubt, is there any difference between magnetic flux and magnetic flux density?

 

[Doc Al]

How come there is magnetic field from loop if there is no current induced in it?

There is a current in the loop, but not an induced current. You need to figure how much current the loop must have to cancel the field from the straight wire.

(Induced current is created by a changing magnetic field -- not relevant here.)

 

[Helly123]

There is a current in the loop, but not an induced current. You need to figure how much current the loop must have to cancel the field from the straight wire.

(Induced current is created by a changing magnetic field -- not relevant here.)

Since the magnetic field H at O is 1.25 A/m
Distance from loop to O is 0.1 m. So current is 12.5 A? Where the current comes from if not induced?

 

[Helly123]

I have a doubt, is there any difference between magnetic flux and magnetic flux density?

I think the wikipedia said so

 

[Doc Al]

Here's how you find the field from a loop of current-carrying wire: Field at Center of Current Loop

Where the current comes from if not induced?

It is added externally. (That loop of wire may be part of a circuit.)

 

[jishnu]

I think the wikipedia said so

Yeah you are right, even though I read it from there could not grasp more idea about that, some please help me with this,
is there difference in their units
Or what makes them different from each other?

 

[Helly123]

Yeah you are right, even though I read it from there could not grasp more idea about that, some please help me with this,
is there difference in their units
Or what makes them different from each other?

The wikipedia explained it too

H units is A/m
B units is Wb/m2

 

[Helly123]

There is a current in the loop, but not an induced current. You need to figure how much current the loop must have to cancel the field from the straight wire.

(Induced current is created by a changing magnetic field -- not relevant here.)

Field from straight wire XY is 1.57 10^-5 Wb/m2
B at loop = $u_o$ I/2R
1.57 10^-5 Wb/m2 =( 4$\pi$ 10^-7 • I ) / 2(0.1)
I = 2.5 A
It is still wrong btw..

 

[Doc Al]

When I solve for B from the straight wire, I get B = 10^-6 T

 

[jishnu]

Is the straight line wire infinitely long?

 

[Doc Al]

Is the straight line wire infinitely long?

That's what I assume.

 

[Helly123]

When I solve for B from the straight wire, I get B = 10^-6 T

How come? $u_0$ I / 2$\pi$r

 

[Doc Al]

How come? $u_0$ I / 2$\pi$r

Oops, my bad. I agree with your result of 1.57 10^-5.

 

[Doc Al]

Field from straight wire XY is 1.57 10^-5 Wb/m2
B at loop = $u_o$ I/2R
1.57 10^-5 Wb/m2 =( 4$\pi$ 10^-7 • I ) / 2(0.1)
I = 2.5 A
It is still wrong btw..

My calculations agree with yours.

 

[Doc Al]

One thing that could explain the discrepancy: They refer to the loop as "doubly-rolled". Does that mean it's really two loops? (Which would make the required current half as much.)

 

[Helly123]

One thing that could explain the discrepancy: They refer to the loop as "doubly-rolled". Does that mean it's really two loops? (Which would make the required current half as much.)

Yes. I think so. So it makes the current flow is 1.25 A for each loop?

 

[Doc Al]

Yes. I think so. So it makes the current flow is 1.25 A for each loop?

Right. (It's one current going through both turns of wire.)

 

[Helly123]

Right. (It's one current going through both turns of wire.)

Awesome. Thanks @Doc Al