# 22.11 More applications of magnetism  (Page 5/12)

 Page 5 / 12

An example of magnetohydrodynamics (MHD) comes from the flow of a river (salty water). This fluid interacts with the Earth’s magnetic field to produce a potential difference between the two river banks. How would you go about calculating the potential difference?

Draw gravitational field lines between 2 masses, electric field lines between a positive and a negative charge, electric field lines between 2 positive charges and magnetic field lines around a magnet. Qualitatively describe the differences between the fields and the entities responsible for the field lines.

## Problems&Exercises

Indicate whether the magnetic field created in each of the three situations shown in [link] is into or out of the page on the left and right of the current.

(a) right-into page, left-out of page

(b) right-out of page, left-into page

(c) right-out of page, left-into page

What are the directions of the fields in the center of the loop and coils shown in [link] ?

What are the directions of the currents in the loop and coils shown in [link] ?

(a) clockwise

(b) clockwise as seen from the left

(c) clockwise as seen from the right

To see why an MRI utilizes iron to increase the magnetic field created by a coil, calculate the current needed in a 400-loop-per-meter circular coil 0.660 m in radius to create a 1.20-T field (typical of an MRI instrument) at its center with no iron present. The magnetic field of a proton is approximately like that of a circular current loop $0\text{.}\text{650}×{\text{10}}^{-\text{15}}\phantom{\rule{0.25em}{0ex}}m$ in radius carrying $1\text{.}\text{05}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}A$ . What is the field at the center of such a loop?

$1\text{.}\text{01}×{\text{10}}^{\text{13}}\phantom{\rule{0.25em}{0ex}}\text{T}$

Inside a motor, 30.0 A passes through a 250-turn circular loop that is 10.0 cm in radius. What is the magnetic field strength created at its center?

Nonnuclear submarines use batteries for power when submerged. (a) Find the magnetic field 50.0 cm from a straight wire carrying 1200 A from the batteries to the drive mechanism of a submarine. (b) What is the field if the wires to and from the drive mechanism are side by side? (c) Discuss the effects this could have for a compass on the submarine that is not shielded.

(a) $4\text{.}\text{80}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}T$

(b) Zero

(c) If the wires are not paired, the field is about 10 times stronger than Earth’s magnetic field and so could severely disrupt the use of a compass.

How strong is the magnetic field inside a solenoid with 10,000 turns per meter that carries 20.0 A?

What current is needed in the solenoid described in [link] to produce a magnetic field ${\text{10}}^{4}$ times the Earth’s magnetic field of $5\text{.}\text{00}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}T$ ?

39.8 A

How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth’s $\left(5\text{.}\text{00}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}T\right)?$ Assume a long straight wire carries the current. (In practice, the body of your car shields the dashboard compass.)

Measurements affect the system being measured, such as the current loop in [link] . (a) Estimate the field the loop creates by calculating the field at the center of a circular loop 20.0 cm in diameter carrying 5.00 A. (b) What is the smallest field strength this loop can be used to measure, if its field must alter the measured field by less than 0.0100%?

(a) $3\text{.}\text{14}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}T$

(b) 0.314 T

Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
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