Question

17.1) Helmholtz coils

The magnetic field on the axis of a circular loop of wire is
not very uniform (in fact, we showed that the field

strength decreases as 1/r3

). But, with two such coils, one can produce a relatively
uniform field in a small

neighborhood.

Consider two parallel circular coils of radius a, centered on
the y-axis. One coil is in the y = 0 plane, and the

other is in the y = d plane. Assume that the current I in each
coil flows in the same direction.

(a) Compute the magnetic field at a point y0, between the
loops, on the y-axis.

(b) At the midpoint between the two coils (i.e., at y0 =

1

2

d), show that the first derivative of the magnetic field

vanishes

dB

dy

y= d

2

= 0. (1)

This means that the field varies very little in the y
direction at this point.

Answer #1

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...

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...

A circular loop with 50 coils is pulled (to the right) from an
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edge of the loop is at the right edge of the magnetic field. After
0.250 seconds the loop has moved completely out of the magnetic
field. Diameter of the coil is 10 cm
Find the rate of change in flux through one loop as the loop if
the loop is pulled out of the...

Helmholtz coils. Sometimes experimenters need to produce a
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wrapping a long straight solenoid around the experiment. Here’s a
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along the axis of a circular conducting loop with radius a and
current I is

A magnetic field, strength 3T, has a direction out of the page.
A loop of wire sits in the field and on the plane of the page (area
vector of loop is out of page). The loop is much smaller than the
extent of the field. The magnetic field starts to slowly change at
a rate of -0.0001T/s. Looking down on the loop, which statement is
correct?
A. Magnetic flux out of page decreasing; anti-clockwise current
induced in loop
B....

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that it cuts through the field's lines. The amplitude of the
induced EMF generated in the coil is 7.9 mV. Which of the following
could be done to INCREASE the amplitude of the EMF
induced in the coil?
a. reshape the coil into a square instead of a circle
b. rotate the coil such that its axis of rotation is parallel to
the magnetic field instead of...

Two closely wound circular coils with centers on a common axis
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The coils are separated by a distance ?, which is assumed to be
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(a) Assuming a current ?1
in coil 1, obtain vector potential ?⃗1at an arbitrary point on coil
2.
(Hint : Use results of a magnetic dipole)
(b) Find the total flux linkage Λ12 at the coil 2
(c)...

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coil?
magnitude:__________ A
What is the direction of the current if the axial component of
the field points away from the viewer?

1. Is the magnetic pole of the Earth nearest the geographic
North Pole a magnetic north or a magnetic south pole?
2. A current in a solenoid coil creates a magnetic field inside
that coil. The field strength is directly proportional to:
a. the coil area
b. the current.
c. Both A and B are valid choices.
d. None of the above choices are valid.
3. A double loop of wire (making 2 turns) is in the xy-plane
centered at...

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