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Diagram showing a zoom in to a magnetohydrodynamic propulsion system on a nuclear submarine. Liquid moves through the thruster duct, which is oriented out of the page. Magnetic fields emanate from the coils and pass through a duct. The magnetic flux is oriented up, perpendicular to the duct. Each duct is wrapped in saddle-shaped superconducting coils. An electric current runs to the right, through the liquid and perpendicular to the velocity of the liquid. The electric current flows between a pair of electrodes inside each thruster duct. A repulsive interaction between the magnetic field and electric current drives water through the duct. An illustration of the right hand rule shows the thumb pointing to the right with the electric current. The fingers point up with the magnetic field. The force on the liquid is oriented out of the page, away from the palm.
An MHD propulsion system in a nuclear submarine could produce significantly less turbulence than propellers and allow it to run more silently. The development of a silent drive submarine was dramatized in the book and the film The Hunt for Red October .

Section summary

  • The magnetic force on current-carrying conductors is given by
    F = IlB sin θ, size 12{F= ital "IlB""sin"θ} {}
    where I size 12{I} {} is the current, l size 12{l} {} is the length of a straight conductor in a uniform magnetic field B size 12{B} {} , and θ size 12{θ} {} is the angle between I size 12{I} {} and B size 12{B} {} . The force follows RHR-1 with the thumb in the direction of I size 12{I} {} .

Conceptual questions

Draw a sketch of the situation in [link] showing the direction of electrons carrying the current, and use RHR-1 to verify the direction of the force on the wire.

Verify that the direction of the force in an MHD drive, such as that in [link] , does not depend on the sign of the charges carrying the current across the fluid.

Why would a magnetohydrodynamic drive work better in ocean water than in fresh water? Also, why would superconducting magnets be desirable?

Which is more likely to interfere with compass readings, AC current in your refrigerator or DC current when you start your car? Explain.

Problems&Exercises

What is the direction of the magnetic force on the current in each of the six cases in [link] ?

Figure a shows the magnetic field B out of the page and the current I downward. Figure b shows B toward the right and I upward. Figure c shows B into the page and I toward the right. Figure d shows B toward the right and I toward the left. Figure e shows B upward and I into the page. Figure f shows B toward the left and I out of the page.

(a) west (left)

(b) into page

(c) north (up)

(d) no force

(e) east (right)

(f) south (down)

What is the direction of a current that experiences the magnetic force shown in each of the three cases in [link] , assuming the current runs perpendicular to B size 12{B} {} ?

Figure a shows magnetic field B out of the page and force F upward. Figure b shows B toward the right and F upward. Figure c shows B into the page and F toward the left.

What is the direction of the magnetic field that produces the magnetic force shown on the currents in each of the three cases in [link] , assuming B size 12{B} {} is perpendicular to I size 12{I} {} ?

Figure a show the current I vector pointing upward and the force F vector pointing left. Figure b shows the current vector pointing down and F directed into the page. Figure c shows the current pointing left and force pointing up.

(a) into page

(b) west (left)

(c) out of page

(a) What is the force per meter on a lightning bolt at the equator that carries 20,000 A perpendicular to the Earth’s 3 . 00 × 10 5 -T size 12{3 "." "00" times "10" rSup { size 8{ - 5} } "-T"} {} field? (b) What is the direction of the force if the current is straight up and the Earth’s field direction is due north, parallel to the ground?

(a) A DC power line for a light-rail system carries 1000 A at an angle of 30.0º to the Earth’s 5.00 × 10 5 -T size 12{5 "." "00" times "10" rSup { size 8{ - 5} } "-T"} {} field. What is the force on a 100-m section of this line? (b) Discuss practical concerns this presents, if any.

(a) 2.50 N

(b) This is about half a pound of force per 100 m of wire, which is much less than the weight of the wire itself. Therefore, it does not cause any special concerns.

What force is exerted on the water in an MHD drive utilizing a 25.0-cm-diameter tube, if 100-A current is passed across the tube that is perpendicular to a 2.00-T magnetic field? (The relatively small size of this force indicates the need for very large currents and magnetic fields to make practical MHD drives.)

A wire carrying a 30.0-A current passes between the poles of a strong magnet that is perpendicular to its field and experiences a 2.16-N force on the 4.00 cm of wire in the field. What is the average field strength?

1.80 T

(a) A 0.750-m-long section of cable carrying current to a car starter motor makes an angle of 60º with the Earth’s 5 . 50 × 10 5 T field. What is the current when the wire experiences a force of 7.00 × 10 3 N ? (b) If you run the wire between the poles of a strong horseshoe magnet, subjecting 5.00 cm of it to a 1.75-T field, what force is exerted on this segment of wire?

(a) What is the angle between a wire carrying an 8.00-A current and the 1.20-T field it is in if 50.0 cm of the wire experiences a magnetic force of 2.40 N? (b) What is the force on the wire if it is rotated to make an angle of 90º size 12{"90"°} {} with the field?

(a) 30º size 12{"30"°} {}

(b) 4.80 N

The force on the rectangular loop of wire in the magnetic field in [link] can be used to measure field strength. The field is uniform, and the plane of the loop is perpendicular to the field. (a) What is the direction of the magnetic force on the loop? Justify the claim that the forces on the sides of the loop are equal and opposite, independent of how much of the loop is in the field and do not affect the net force on the loop. (b) If a current of 5.00 A is used, what is the force per tesla on the 20.0-cm-wide loop?

Diagram showing a rectangular loop of wire, one end of which is within a magnetic field that is present within a circular area. The field B is oriented out of the page. The current I runs in the plane of the page, down the left side of the circuit, toward the right at the bottom of the circuit, and upward on the right side of the circuit. The length of the segment of wire that runs left to right at the bottom of the circuit is twenty centimeters long.
A rectangular loop of wire carrying a current is perpendicular to a magnetic field. The field is uniform in the region shown and is zero outside that region.

Questions & Answers

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
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Dominic
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
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Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
×/×+9+6/1
Debbie
Q2 x+(x+2)+(x+4)=60 3x+6=60 3x+6-6=60-6 3x=54 3x/3=54/3 x=18 :. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
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Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
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divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
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Mark
16
Makan
x=16
Makan
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
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Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
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Opoku
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Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
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Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
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how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
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Source:  OpenStax, College physics (engineering physics 2, tuas). OpenStax CNX. May 08, 2014 Download for free at http://legacy.cnx.org/content/col11649/1.2
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