Physics question

Question

Which of the following would increase the current induced in a coil of wire when you move a magnet through the coil?

A. Making the coils larger in size

B. Increasing the number of coils

C. Moving the magnet through the coils faster.

D. All of the above will increase the current induced in the coil

Answer 1

Hi Jessica G., An interesting question, and a little involved to fully understand. Read on!

It's only C.

Let's look at (A) first. Remember that the force on an electron in the wire is proportional to the rate of change of the total amount of magnetic field (flux) present in the loop. That's a different concept, by the way, from the magnetic field strength B present at a point! Flux is the sum of all those B values across an area, in this case the plane enclosed by the loop. [To be exact, the sum of the portion of that magnetic field perpendicular to the surface.] You MUST understand that distinction before proceeding further!!

Call the distance from the center of the magnet out its end and through the loop as d, and the radius of the loop as r. (Draw a sketch to help visualize). We usually visualize magnetic field as looped lines of the field, but realize that the magnetic field is continuous, it exists even at places where we don't explicitly draw a line; we use the lines to help us remember its direction and strength, and to view trends in strength and direction of it.

Set the bar magnet with d a little greater than 1/2 the length of the magnet, so that it is near (but not inside) the loop, and then vary the diameter of the loop from very small r to greater r. You will see that as the loop gets wider it will take in more flux for a while; then it starts to get "outside" that forward-directed portion of the magnetic field from the magnet (at the transition point, the magnetic field is directed radially across the loop), and the field locally starts pointing backwards rather than forwards, so that the total flux going through the loop in the forward direction starts dropping off again. Since the total flux has gone down, therefore the rate of change if the magnet were twitched a little must go down too, since the present-condition flux is the sum of the flux change from a value of zero (with very large d, the magnet far away) to the present value of the flux with the present value of d, and if that sum has gone down then all the pieces of it (bits added as d has decreased from infinity) have also decreased.

Another way of thinking of this is to put the coil around the middle of the magnet and ask, how much of the flux generated by the magnet is still outside the coil? Since as the coil is made wider, i.e. further and further away from the sides of the magnet, more and more of the magnetic field is as loops completely inside the coil, therefore the total flux outside (in the plane, but outside the loop) must have gotten smaller. That amount of flux "outside" is equal to the negative of the net amount of flux inside: it represents the portion of flux which went up through the magnet body, but did not return still inside the loop.

So that was a very long way of showing, that the induced current must be smaller for some configurations of loop and magnet, as the coil diameter is increased, hence it's incorrect to say that increasing the loop diameter ALWAYS increases the current. That disposes of choice (A).

Choice (C) you know must be true, since the rate of change of flux is linearly proportional to the force generated on each electron, so increase the rate of change of flux by moving the magnet through faster, and the current steps up.

Choice (B) is a little contraintuitive to understand. If you are pushing an electron down one wire loop, does that affect what happens to an electron in another, series-linked wire loop? In most experimental setups, it does: if the induced current is led out through a light bulb, for example, pushing electrons at two separate places in a circuit will give them twice the voltage, and therefore twice the amount of current may (briefly, because the induced current is a transient effect) flow. Or if the loop is an open-circuit, the voltage generated between the wire ends will increase with number of loops (though this is voltage, not current per se). However, IF the loop is a closed, short-circuit series-connected-loops device, then the resistance of the circuit is proportional to the length of wire, and as the number of loops is increased, that closed-circuit current WILL NOT CHANGE, because the resistance steps up linearly with the induced voltage. Therefore, the current will not depend on the number of loops IN ALL CIRCUMSTANCES, and (B) is false.

I can hear you moaning, "Do I always have to consider all possible cases in these questions?". Yes, you do, that's just how multiple choice questions are written, for standardized tests.

And to put that in a broader context, remember what happened to the space shuttle Challenger, when the possibility of an O-ring failure on the rocket was considered and then disregarded upon transfer of information up the management tree as a remote-possibility circumstance? (if you don't immediately recall, see https://en.wikipedia.org/wiki/Space_Shuttle_Challenger_disaster ).

-- Hope this makes better sense to you now,

-- Cheers, -- Mr. d.