Direction of the Magnetic Field at a Point

[ktjj4]

Homework Statement

The problem asks to find the direction of the magnetic field at point P, which is at the center of 2 separate semi-circle wires that form a circle. The current in each wire flows in the same direction (to the right). I attached a picture below.

Homework Equations

The Attempt at a Solution

I used the right hand rule for curved loops where your fingers curve in the direction of the current and your thumb points in the direction of the magnetic field.

I know the answer is that at point P, the magnetic field points into the page, but I don't understand.

When I use the right hand rule, for the top wire, my thumb points into the page, so does that mean the magnetic field for that wire points into the page in the area inside the circle and points out of the page above the top wire? And for the bottom wire, my thumb points out of the page, so does that mean that the magnetic field points out of the page in the area inside the circle and points into the page below the bottom wire?

This should be simple, but I feel as though I'm missing a piece of information.

Thank You

 

[Orodruin]

I know the answer is that at point P, the magnetic field points into the page, but I don't understand

Are you sure about this?

 

[ktjj4]

Are you sure about this?

I mean, if I remember correctly, it is what my professor said.

 

[Orodruin]

I mean, if I remember correctly, it is what my professor said.

Well, it is not correct. At least not for the case of $I_1 = I_2$ that is mentioned in the image.

 

[ktjj4]

Well, it is not correct. At least not for the case of $I_1 = I_2$ that is mentioned in the image.

That's the second part of the question. The first part just asks for the direction considering that the two currents are different.

 

[Orodruin]

That's the second part of the question. The first part just asks for the direction considering that the two currents are different.

Then it depends on the relation between the sizes of the currents.

 

[ktjj4]

Then it depends on the relation between the sizes of the currents.

Oh, does that mean that the bigger current dictates the direction of the magnetic field at point P?

So, if the current in the top wire is greater than the bottom wire, the direction of the field at P is into the page, but if the current in the bottom wire is greater, then the direction is out of the page?

What if the currents were the same then?

 

[Orodruin]

So, if the current in the top wire is greater than the bottom wire, the direction of the field at P is into the page, but if the current in the bottom wire is greater, then the direction is out of the page?

Yes.

What if the currents were the same then?

You tell me. What do you think?

 

[ktjj4]

Yes.You tell me. What do you think?

I think I got it; so if I were to use Biot-Savart's law, the currents would end up cancelling each other out, no? And if there's no current, there's no field. So no direction.

 

[Orodruin]

I think I got it; so if I were to use Biot-Savart's law, the currents would end up cancelling each other out, no?

More precisely: The magnetic field from each of the currents would cancel out. Your conclusion is correct.

 

[ktjj4]

More precisely: The magnetic field from each of the currents would cancel out. Your conclusion is correct.

Oh ok, thanks for the help :)