Question

Helmholtz coils. Sometimes experimenters need to produce a magnetic field that is constant over some region of space, without wrapping a long straight solenoid around the experiment. Here’s a good way to do that. a. Show that the magnetic field a distance z along the axis of a circular conducting loop with radius a and current I is

Answer #1

Helmholtz coils are frequently used in experiments because they
create a uniform magnetic field about their axial direction. For
example, they are traditionally used in the experiment for the
measurement of the charge to mass ratio of the electron. Helmholtz
coils are two coils separated by a distance equal to their radius
and also carry equal currents in the same direction, as shown in
the figure on the right. Suppose the radius of the coils is 12.00
cm, each coil...

Helmholtz coils are a method developed to provide a uniform
magnetic field in a small region. They are constructed by placing
two identical wire loops parallel to each other, separated by a
distance equal to their radii, as shown in the Figure. Assume that
the two loops are also connected in parallel to a power supply, so
that they produce the same field.
(a) Find the length of a 28-gauge copper wire that will produce a
75 Ω coil.
m...

If you pass a current through a wire, you can create a magnetic
field. In this class we examine the field from three specific
configurations: an infinitely-long straight wire, a compact loop of
wire (possibly with multiple turns, a coil), or an infinitely long
solenoid (think of an infinitely-long cylinder of loops made by
wrapping a single wire). See the text for an extended description
of all three geometries.
Here’s the challenge: there are three slightly different formulas
used to...

(a) The magnetic field produced by the loop decreases further
away from the loop. We can
define an “effective distance” as how far along the z axis you must
move from the center of the
loop in order for the magnetic field to decrease to half its value
at the center of the loop. What is
the effective distance for the magnetic field of the loop? Compare
the effective distance to the
radius of the loop.
(b) What data collected...

Written Problem: Induction from a falling
magnet
We have a small magnet with a magnetic moment of m = 0.1
Am2 (remember: magnetic moment is defined as m = IA -
see page 932 of book for the definition). We also have coils of
wire. The coils are made out of 100 circular loops of a single
wire. A single loop has a radius of 10 cm. The thickness of the
wire has a circular cross section with a 0.5...

1. Which describes the vector calculation of the Biot-Savart
law?
a. The length element in the direction of the
current is crossed into a vector directed from that element toward
the point of measurement.
b. The length element in the direction of the current
is dotted into a vector directed from that element toward the point
of measurement.
c. The magnetic field vector is crossed into a vector
directed from a current-length element toward the point of...

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