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

[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