Physics 2020
Prof. Steven Pollock
20-6
Example: A current flows around a ring (a loop), and then
(Side view)
Rule #2:
Can you verify this with the Right Hand Rule?
B-fields exert a force on currents. If you put a current
(I) into some external B-field, the current is pushed.
Magnitude of force:
F=I l B sin
I = current (in Amps)
B = strength of B-field
l = length of the wire in B-field
Angle between I and B
Direction of force: “2nd right hand rule”
n
n
n
Point your right-hand fingers in the direction of I.
Orient so your fingertips curl naturally towards B.
Stick out your thumb. It points in the direction of F.
In the picture above, F points
out of the page.
(Convince Yourself!!)
Physics 2020
Prof. Steven Pollock
20-6
(Note: F is perpendicular to B, and to I)
When a current flows around a ring, RHR #1 tells you the direction
of the resulting (“induced”) B.
Some people introduce another “Right Hand
Rule,” which we might call “Right Hand
Rule #1b”
n
If your right hand fingers curl with the current in a current loop,
your thumb points in the direction of the B.
This is different than the RHR#1, where your thumb pointed with
I, and your fingers pointed like B! So don’t mix them up! You
never need RHR #1b, I just find it quicker and easier when you
have current loops to deal with.
Physics 2020
Prof. Steven Pollock
If θ = 90, F is max
20-7
Fmax = IlB
e.g.
So B = Fmax/Il.
This in fact defines the value of B!
Units [B] = N/A*m = 1 Tesla = T
F=
into page
Convince Yourself!
1 Tesla is a lot. The Earth’s natural field is B about 0.5 * 10^-4 T.
n
An old unit for B was “Gauss,” 1 Gauss = 10^-4 T
n
So Bearth = 0.5 Gauss
n
Kitchen magnets are around 50G or 5*10^-3 T = 5mT
n
Industrial magnets = 1 or 2 T (that’s a natural limit for Iron)
(This is a typical NMR field)
n
Superconducting magnets around 20T
Ex.) Take a “horseshoe magnet” (Big B-field between poles,
remember B points from N towards S) run a current, I, into the
page in this big B field: (I used a dot in the figure: TYPO! I meant
to use an "x" there, and can't fix it now,
sorry) RHR#2 says F is up (convince yourself!).
F=IlB
(The length of the wire that is in the Bfield)
Physics 2020
Prof. Steven Pollock
20-8
Example: Take that horseshoe magnet and orient it so “N” is in
front of the page, “S” is behind. So B points into the page.
Now lower a current carrying loop of wire into this Bfield.
B-field is localized
to this region here.
There will only be
Forces where the
wire is in the B-field.
Use the 2nd RHR, and convince yourself they look alike.
The forces on the left
& right cancel, there
is a net force down.
Easily measured with a scale. The current loop is “sucked in” to
this particular B-field.
If
I=20A, (Typical large current in household wires)
l=10cm, (Typical large horseshoe magnet width)
B=1T (A very strong Fe magnet!)
F=I l B=(20A)(.1m)(1N/Am)=2N.
Not huge, but you could easily feel this. (This is one technique to
measure a B-field.)
Physics 2020
Prof. Steven Pollock
20-9
This force has nothing to do with the metal of the wire. It is really
the moving charges (the current) that feels this force.
E.g. A beam of protons flying through B would also feel the
magnetic force, even though there’s no wire around at all.
F=(I)(l)(B)sinθ
Our formula for a wire.
F=qVBsinθ
The formula for individual particles.
Where V=velocity of the particle. It’s the same formula!
Because: I=Nq/t = #charges/sec
V = l/t = dist/time
So I*lB = (Nq/t)(l)(B) = Nq*VB (i.e. each charge feels qVB, so
all N charges feel NqVB)
The direction is just as before (2nd RHR) Except if the q’s are
negative, the direction of F must be reversed! So e.g.
F on +q is up (e.g. protons)
F on –q is down (e.g. electrons)