Struggling To Study: 10+ Hours and No Easy Answers

[exitwound]

I have the answer to this. It's not a homework problem. Just attempting to study. Isn't going so well. You'd think after 10+ hours of it, I'd be able to solve the 'easy' level problems in the book.

Homework Statement

Homework Equations

$$\phi = \int \vec B \cdot d \vec a$$
$$E= -\frac{d\phi}{dt}$$
$$E=\frac{i}{R}$$

The Attempt at a Solution

I know that at t=0, E=iR, E=(5A)(4Ohm)=20V.

I don't know even how to start this problem.

 

[buffordboy23]

Think about the magnetic field due to a long straight wire with constant current and relate this to the magnetic flux through the upper and lower halves of the semicircle. Since we have a changing current, the magnetic field around the long wire will change but what about the flux? Symmetry is a key principle in solving this problem.

 

[exitwound]

B above the long straight wire is out of the page and B below the long straight wire is into the page.

Flux is B.A so the flux thru each hemisphere is the same as the other, only in opposite direction.

Other than that, I'm still lost. This chapter is impossible to understand.

 

[buffordboy23]

Exactly. You are glimpsing at the symmetry involved in this problem. What is the net flux then? If we change the current with time, sure we change the magnetic field but what about the net flux?

 

[exitwound]

Complete guess. If the current in the wire is decreasing with time, then the flux is too.

 

[buffordboy23]

That makes sense, sure. But what is the definition of flux? We have magnetic field vectors going through the circular hoop in opposite directions; some go into the page, some go out of the page. Think about this, the net flux and symmetry.

 

[exitwound]

I don't know what you're getting at.