Question

16. To generate a uniform 2T magnetic field for an MRI machine with a coil of diameter 50 cm and 10 000 turns over the 1 m distance of the coil,

(a) Solve for the current through the coil needed to create this large magnetic field. /2

(b) Approximate the total length of wire needed to produce 10 000 turns of this radius. /2

(c) If we need to keep the resistive power emitted by this coil under 1000 W so that the patient is not uncomfortable, what is the maximum resistance allowable by the coil? /2

(d) If the cross-sectional area of the wire used is 7.85 ×10−9 m2 , find the maximum resistivity of wire that could be used to meet your criterion found in part (c). /2 15

(e) Copper has one of the lowest room temperature resitivities of all metals at ρ = 1.7 × 10−8Ω m. Could an MRI machine with these requirements be made to operate with copper wire at room temperature as its coil? How is this avoided in real MRI machines?

Answer #1

16. To generate a uniform 2T magnetic field for an MRI machine
with a coil of diameter 50 cm and 10 000 turns over the 1 m
distance of the coil,
(a) Solve for the current through the coil needed to create this
large magnetic field. /2
(b) Approximate the total length of wire needed to produce 10
000 turns of this radius. /2
(c) If we need to keep the resistive power emitted by this coil
under 1000 W...

To generate a uniform 2T magnetic ﬁeld for an MRI machine with a
coil of diameter 50 cm and 10 000 turns over the 1 m distance of
the coil,
(a) Solve for the current through the coil needed to create this
large magnetic ﬁeld.
(b) Approximate the total length of wire needed to produce 10 000
turns of this radius.
(c) If we need to keep the resistive power emitted by this coil
under 1000 W so that the...

A copper coil with 30 turns and radius 10 cm has a magnetic
field going through it which changes in time according to the
formula B = 5e-0.3t Tesla. The radius of the wire is 0.24 mm and
the resistivity of copper is 1.68 x 10-8 Ωm.
(a) Calculate the induced voltage in the coil at 4 seconds.
(b) Calculate the induced current in the coil at 4 seconds.

A copper coil with 30 turns and radius 10 cm has a magnetic
field going through it which changes in time according to the
formula B = 5e-0.3t Tesla. The radius of the wire is
0.24 mm and the resistivity of copper is 1.68 x 10-8
Ωm.
(a) Calculate the induced voltage in the coil at 4 seconds.
(b) Calculate the induced current in the coil at 4 seconds.

1.The magnetic field produced by the solenoid in a magnetic
resonance imaging (MRI) system designed for measurements on whole
human bodies has a field strength of 8.19 T, and the current in the
solenoid is 2.10 × 102 A. What is the number of turns per meter of
length of the solenoid?
You have a wire of length L = 1.0 m for making a square
coil of a dc motor. The current in the coil is I = 2.0...

The magnetic field perpendicular to a single 14.2-cm-diameter
circular loop of copper wire decreases uniformly from 0.670 T to
zero. If the wire is 2.75 mm in diameter, how much charge moves
past a point in the coil during this operation? The resistivity of
copper is 1.68×10−8Ω⋅m. Express your answer to three significant
figures and include the appropriate units.

The magnetic field perpendicular to a single 15.7-cm-diameter
circular loop of copper wire decreases uniformly from 0.550 T to
zero.
If the wire is 2.75 mm in diameter, how much charge moves past a
point in the coil during this operation? The resistivity of copper
is 1.68×10−8Ω⋅m. Express your answer to three significant figures
and include the appropriate units.

In each of the following situations, a coil rotates in a uniform
magnetic field. Rank the coils in order of the maximum
value of the alternating emfinduced in the coil, from greatest
value to smallest value.
(i) A coil with 500 turns and area 2.00 * 10–3
m2 rotates at 50.0 rad/s in a magnetic field of
magnitude 5.00 * 10–3 T.
(ii) A coil with 400 turns and area 2.00 * 10–3
m2 rotates at 70.0 rad/s in a...

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...

For a class demonstration, a professor needs to create a
solenoid using copper wire with diameter d = 0.500 mm. The
resistance of the solenoid needs to be 3.30 Ω and the magnetic
field of the solenoid with a current of 2.90 A should be 5.70 ✕
10−2 T. Assume the resistance does not change significantly with
temperature, and the radius of the solenoid is 1.00 cm. (Use ρ =
1.70 ✕ 10−8 Ω · m for the resistivity of...

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