Find the current induced in a wire loop by a nearby current

[BvU]

What makes the sign different? Since, B, v still the same?

Going round the loop, emf = V_AB+V_CD = V_AB-V_DC

And where the 'b' comes from the options?

Do the math and post...

What makes the wire have magnetic force?

The free charge carriers in the wire can move under the influence of the force. The Lorentz force is the underlying phenomenon. It's extremely important in physics. As to the 'why?' of the Lorentz force: you can dig deeper into the fundamentals of electrodynamics, but a 'why?'question is ultimately not answerable. Physicists restrain themselves and search for the 'how?'.

Why the question said that the magnetic flux density is negligible?

It did not. It only said you don't have to take into account the magnetic field due to the current in the loop. The whole exercise can also be done by determining the magnetic flux through the loop (the flux due to $I$ in the long wire ) and applying Faraday's law.

 

[Helly123]

Thanks for the explanation. Why going in loop make different sign?

 

[Helly123]

#22:
The 'almost' was because of the sign. It is opposite to that induced in AB.

#25:
No. Velocity $\vec v$ and magnetic field $\vec B$, are both perpendicular to the resulting force $F$.
Not what I meant. What I meant is: one doesn't want to confuse oneself unnecessarily by looking at negatively charged moving charge carriers. So if a current $\vec I$ is given, work with positive charge carriers moving in that direction.

The Lorentz force $\ \vec F = q(\vec E + \vec v\times \vec B)\$ works on ALL charges, negative (q<0) or positive (q>0)
( also on neutral charges (q=0) )

Motion of charge produces a magnetic field.
Positive charges move under the influence of a Lorentz force -- if they can. In a conductor (a wire), the positive charge carriers generally are not free to move. Electrons, the negative charge carriers, can move and thereby generate an emf.

I think I understand what you are trying to say here (correct me if I miss): Lorentz force on CD pushes electrons down and positive ions up. Positive ions can't move, electrons can. They don't move without limits (they don't pile up because they repel each other, and there is a resistance)​

#26: The exercise in post 1 gives a current $I$ in the long wire and asks for the current in loop ABCD; with resistance $R$ given, that is equivalent to asking for the emf divided by $R$.

#27:
They do not. Their net charge is 0.
No. Their direction of motion is the direction of $\vec v$. Their orientation is perpendicular to $\vec V$.

What is their orientation? From high potensial to low?

 

[BvU]

#33: Sorry, I meant a lower case velocity vector $\vec v$
All wires are in the plane of the paper. Orientation of section AB is perpendicular to $\vec v$. Same with CD. But both move with velocity vector $\vec v$.

Magnetic field from $\vec I$ is into the paper. Vector cross product $\ \vec v \times \vec B \$ is upwards (same direction as $\vec I\;$), both in AB and in DC. AB is stronger (closer to $\vec I\;$) so netto^* the emf in the loop causes a clockwise (ABCD) current.

^*Going round the loop means add up

V_AB + V_BC + V_CD + V_DA =
V_AB + 0 + V_CD + 0 = V_AB - V_DC​

 

[Helly123]

Yes. But why Vcd become negative?

 

[BvU]

You mean V_DC = - V_CD ? Are you asking about the behavour of a potential difference ?

 

[Helly123]

You mean V_DC = - V_CD ? Are you asking about the behavour of a potential difference ?

Yes. Please

 

[BvU]

$$V_{DC} = V_D - V_C \\
V_{CD} = V_C - V_D \\
V_D - V_C = -\left ( V_C-V_D \right) \Rightarrow V_{DC} = - V_{CD}$$

 

[BvU]

Make a diagram indicating polarities to see that the induced voltages push in the same direction, therefore in opposite directions in the loop

 

[Helly123]

What is polarities diagram?

 

[Helly123]

Current CD is different direction than AB
But why the way we calculate current different than circuit connected to battery or any voltage source?

 

[BvU]

Current CD is different direction than AB

Right

But why the way we calculate current different than circuit connected to battery or any voltage source?

We do it exactly the same way:

[edited: this way it corresponds to the picture in post #1]

 

[Helly123]

I cannot put it as solved. Why there is no current in BC and DA?
Emf = Blv sin theta

 

[BvU]

What is $\theta$ ?

There is current, of course (or else there would be an accumulation of charge and you can't have that if there is a conductor in between).

 

[Helly123]

What is $\theta$ ?

There is current, of course (or else there would be an accumulation of charge and you can't have that if there is a conductor in between).

Theta is between v and length or the wire?
If yes, 90 degree is for AB and CD
And 0 for BC and DA

Because the B going into the page and v to left

 

[BvU]

Yes, in a way. Check the links in #24. The underlying expression is the Lorentz force:$$\vec F = q\, \left (\vec E + \vec v \times \vec B \right )$$so in BC the emf is indeed perpendicular to the direction of the wire.

and v to left

I have a distinct memory that $\vec v$ is to the right, but PF doesn't want to show the picture in #1 at this moment