I would like to have clarified a number of points regarding the Magnetism slides.
1) Regarding B and decrease of B as distance from I increases.
The relationship between B and distance from I (r) is B ~ 1/r (re: Capa 8 q 1a). However, in the class slides (slide 1 p. 4) it says
" delta B ~ 1/r2 (r squared)"
What r is this? I notice this is not the perpendicular r, but in the following delta B equation, sin theta is multiplied, and thus becomes the perpendicular r. Confusion?
2) Slide 2 p. 5, for a circular clockwise I, P1 within the circle points into the page, while P2 outside the circle points out of the page. Is it that B's outside a circular I are always in the opposite direction as that in the I?
3) slide 4 p. 3. The current loops in the diagram show a B opposite to RHR. Is it because the loops are electron orbitals, and electrons produce B's opposite to RHR?
4) similar question as previous. slide 1 p. 6. why is the B opposite to the RHR?
Thank you.
Regarding your first question, while there is an apparent inconsistency here, both are correct. The problem is one expression is for "B" and one is for "ΔB". To get B~1/r you have to integrate "ΔB" over the particular geometry appropriate to the problem. This is why you get different expressions for the B-field generated by current in a straight wire, a loop of wire, etc.
The "r" being referred to for "ΔB" is the distance from the point on the wire generating the field when integrating. Since all parts of the wire contribute to the magnetic fields in all parts of space you have to consider "off-axis" contributions as well as those perpendicular. Once the expression is integrated, for example in the case of a straight current carrying wire, the r will refer to the perpendicular distance away since the field will be symmetric and constant along the length of the wire anyhow. Otherwise, it might be important!
For your second question, I assume you are using a right hand rule where you curl your fingers in the direction of the current and your thumb tells you the direction of the magnetic field inside the loop. You can also point your thumb in the direction of the current and curl your fingers around to determine the direction of the magnetic field around the wire. If you do this you will quickly see that your fingers point up on the outside of the loop and down on the inside of the loop no matter what part of the loop you look at. And yes, the field should point in the opposite direction on the outside of the coil compared to the inside. This is because magnetic field lines must always close (the field lines would look like rings around the loop). It might help you to take a look at The "Right-hand Rules" and Magnetic fields.
For the last two questions, so far as I can tell, the directions are as given by the RHR. Pg. 3 slide 1, I get B pointing right, and for slide 4, I get B pointing left. It's not so easy to see which way the loops are supposed to be coming out of the page... look for where the breaks in lines are, indicating that that part of the line is passing behind another line.
Hope that helps!
