Magnetic fields: clearing up some confusion

difference between magnetic field and B-field? What 's the difference between those two?

why the direction of magnetic field of a loop is a circle and the professor use the word" B field" to refer to the direction at a certain point which is tegant to the circle?

Magnetic field and "B-field" are the same. Since we usually use "B" to denote magnetic field, we sometimes refer to the magnetic field as the "B-field". Consider it physics slang. As confusing to the uninitiated as OMG, LOL. ;)


Now, for you second question, if we consider the magnetic field around a current carrying wire, we know that the magnetic field forms a closed loop around the wire. But the magnetic field is a vector, right? So those vectors are tangential to these magnetic field lines and represent the vector field. Those lines just make it a little easier to visualize (without too many crazy arrows all over the place, because I drew 3 and that doesn't look too bad, but to truly represent it we need one for every point along that circle as finely as we are interested in).

to clarify the meaning of "perpendicular distance" when talking about B-fields.

perpendicular distance is the distance from the wire to the point in the magnetic field we are interested in (the angle between this line and the wire does not have to be 90).

Please correct if needed.

The perpendicular distance does indeed need to be perpendicular. I think you are still referring to the magnetic field from a straight segment of wire. In this case, the magnetic field produced is uniform along the wire, and varies radially away from it (~1/r). Since the only variation is radially, you only need this radial distance (which is always perpendicular to the wire).

Please let me know if you are concerned about a different situation.

Force of B-Field of one current-carrying wire on another.

Example: one horizontal wire (I1) has a current flowing to the right. Another, perpendicular to it, is above it with a current flowing upwards. The direction of the force of I1 is downward, by RHR. But, the direction of the force acting on I2 is to the right, because, though the direction of B1 is taken into consideration, the direction of the force is based on the direction of I2 and not I1. Why?

Ahh! But you have already taken into account the direction of I₁ when determining the direction of the magnetic field (B₁) produced by it. You then consider the force exerted by this magnetic field on the second wire, so you must then consider the direction of I₂.

I hope that clears up some confusion concerning magnetic fields.

Question: clarification of lecture notes on magnetic fields

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!

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Question: Induced EMF coil-solenoid; How do areas play a role?

If a coil is placed around a solenoid that has a fluctuating current, how do the radii of the coil and solenoid (so basically, the areas) affect the induced EMF in the coil? Thanks.

Thanks for your question.

The EMF induced in the outer coil is a result of the magnetic field produced in the solenoid.

First let's consider the magnetic field produced by the solenoid, which is given by:

B=μnl

where n is the number of turns/unit length. But wait! There's no mention of area here... in fact as long as the approximation that l>>r holds (and that you are not near the ends), the magnetic field generated by a solenoid is independent of the cross-sectional area.

So let's consider the EMF induced in the coil surrounding the solenoid. This is given by:

EMF=-ΔΦB/Δt=-A_{perpendicular}ΔB/Δt

So the cross-sectional area of the coil does enter into the induced EMF.

Hope that is helpful. For a related question check out: Question: Solenoid in a coil

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Question: Solenoid in a coil

If a solenoid is placed inside a coil, how does the current flowing through it affect said coil? How would you find the inductance value for the coil?

That's a very good question. Qualitatively, the solenoid (with some current running through it) establishes a magnetic field parallel to the axis of the solenoid. If a coil is then placed on the outside of it, the coil will "sense" the magnetic field established by the solenoid. If the current in the solenoid is time-varying (changing in time) then the magnetic field established by it will also change with time. The coil will then "sense" this changing magnetic field and respond to oppose the change (Lenz's law).



Quantitatively, we will have to look at what the magnitude of the magnetic field produced by the solenoid is, and how that may depend on time. The magnetic field of a solenoid is given by:

B_sol=μ₀I[N/l]

Thus, if the current, I is a function of time, the magnetic field will have the same time dependence. If, say, the time dependence is linear (eg. we ramp up the current to the solenoid at a constant rate), then we can use the slope as ΔB/Δt, which is related to the EMF:

EMF=-ΔΦ_B/Δt=-A_{perpendicular}ΔB/Δt

Chapter 21, Question #80 is an example of this, and might be good to look at.

I hope this is helpful and answers your question.

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