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  4. Magnetic forces and fields
  5. Magnetic fields and lines

11.2 Magnetic fields and lines  (Page 3/8)

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Significance

The cross product in this formula results in a third vector that must be perpendicular to the other two. Other physical quantities, such as angular momentum, also have three vectors that are related by the cross product. Note that typical force values in magnetic force problems are much larger than the gravitational force. Therefore, for an isolated charge, the magnetic force is the dominant force governing the charge’s motion.

Check Your Understanding Repeat the previous problem with the magnetic field in the x -direction rather than in the z -direction. Check your answers with RHR-1.

a. 0 N; b. 2.4 × 10 −14 k ^ N ; c. 2.4 × 10 −14 j ^ N ; d. ( 7.2 j ^ + 2.2 k ^ ) × 10 −15 N

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Representing magnetic fields

The representation of magnetic fields by magnetic field lines    is very useful in visualizing the strength and direction of the magnetic field. As shown in [link] , each of these lines forms a closed loop, even if not shown by the constraints of the space available for the figure. The field lines emerge from the north pole (N), loop around to the south pole (S), and continue through the bar magnet back to the north pole.

Magnetic field lines have several hard-and-fast rules:

  1. The direction of the magnetic field is tangent to the field line at any point in space. A small compass will point in the direction of the field line.
  2. The strength of the field is proportional to the closeness of the lines. It is exactly proportional to the number of lines per unit area perpendicular to the lines (called the areal density).
  3. Magnetic field lines can never cross, meaning that the field is unique at any point in space.
  4. Magnetic field lines are continuous, forming closed loops without a beginning or end. They are directed from the north pole to the south pole.

The last property is related to the fact that the north and south poles cannot be separated. It is a distinct difference from electric field lines, which generally begin on positive charges and end on negative charges or at infinity. If isolated magnetic charges (referred to as magnetic monopoles ) existed, then magnetic field lines would begin and end on them.

An illustration of magnetic field lines for three configurations. Figure a shows a bar magnet with a north and south pole. The field lines come out of the north pole and curve out and around to the south pole. Figure b shows north and south poles separated by a gap. The field lines again come out of the north pole, curve out, and enter the south pole. The lines are denser in the gap, and less dense outside. Figure c shows two north poles separated by a gap. Field lines come out of both poles and curve outward. The lines coming out of each pole appear as if the repel the lines coming from the other pole.
Magnetic field lines are defined to have the direction in which a small compass points when placed at a location in the field. The strength of the field is proportional to the closeness (or density) of the lines. If the interior of the magnet could be probed, the field lines would be found to form continuous, closed loops. To fit in a reasonable space, some of these drawings may not show the closing of the loops; however, if enough space were provided, the loops would be closed.

Summary

  • Charges moving across a magnetic field experience a force determined by F → = q v → × B → . The force is perpendicular to the plane formed by v → and B → .
  • The direction of the force on a moving charge is given by the right hand rule 1 (RHR-1): Sweep your fingers in a velocity, magnetic field plane. Start by pointing them in the direction of velocity and sweep towards the magnetic field. Your thumb points in the direction of the magnetic force for positive charges.
  • Magnetic fields can be pictorially represented by magnetic field lines, which have the following properties:
    1. The field is tangent to the magnetic field line.
    2. Field strength is proportional to the line density.
    3. Field lines cannot cross.
    4. Field lines form continuous, closed loops.
  • Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles.

Conceptual questions

Discuss the similarities and differences between the electrical force on a charge and the magnetic force on a charge.

Both are field dependent. Electrical force is dependent on charge, whereas magnetic force is dependent on current or rate of charge flow.

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(a) Is it possible for the magnetic force on a charge moving in a magnetic field to be zero? (b) Is it possible for the electric force on a charge moving in an electric field to be zero? (c) Is it possible for the resultant of the electric and magnetic forces on a charge moving simultaneously through both fields to be zero?

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Problems

What is the direction of the magnetic force on a positive charge that moves as shown in each of the six cases?

Case a: B is out of the page, v is down. Case b: B is to the right, v is up. Case c: B is in, v is to the right. Case d: B is to the right, v is to the left. Case e: B is up, v is into the page. Case f: B is to the left, v is out of the page.

a. left; b. into the page; c. up the page; d. no force; e. right; f. down

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Repeat previous exercise for a negative charge.

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What is the direction of the velocity of a negative charge that experiences the magnetic force shown in each of the three cases, assuming it moves perpendicular to B ?

Case a: B is out of the page, F is up. Case b: B is to the right, F is up. Case c: B is into the page, F is to the right.

a. right; b. into the page; c. down

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Repeat previous exercise for a positive charge.

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What is the direction of the magnetic field that produces the magnetic force on a positive charge as shown in each of the three cases, assuming B → is perpendicular to v → ?

Case a: v is up, F is to the left. Case b: v is down, F is into the page. Case c: v is to the left, F is up.

a. into the page; b. left; c. out of the page

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Repeat previous exercise for a negative charge.

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(a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a 0.500-μC charge and flies due west at a speed of 660. m/s over Earth’s south magnetic pole, where the 8.00 × 10 −5 − T magnetic field points straight up. What are the direction and the magnitude of the magnetic force on the plane? (b) Discuss whether the value obtained in part (a) implies this is a significant or negligible effect.

a. 2.64 × 10 −8 N ; b. The force is very small, so this implies that the effect of static charges on airplanes is negligible.

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(a) A cosmic ray proton moving toward Earth at 5.00 × 10 7 m/s experiences a magnetic force of 1.70 × 10 −16 N . What is the strength of the magnetic field if there is a 45º angle between it and the proton’s velocity? (b) Is the value obtained in part a. consistent with the known strength of Earth’s magnetic field on its surface? Discuss.

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An electron moving at 4.00 × 10 3 m/s in a 1.25-T magnetic field experiences a magnetic force of 1.40 × 10 −16 N . What angle does the velocity of the electron make with the magnetic field? There are two answers.

10.1 ° ; 169.9 °

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(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than 1.00 × 10 −12 N . What is the greatest the charge can be if it moves at a maximum speed of 30.0 m/s in Earth’s field? (b) Discuss whether it would be difficult to limit the charge to less than the value found in (a) by comparing it with typical static electricity and noting that static is often absent.

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Questions & Answers

what does the ideal gas law states
Joy Reply
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
Kate Reply
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Kate Reply
what is the change in momentum of a body?
Eunice Reply
what is a capacitor?
Raymond Reply
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
Maria Reply
please solve
Sharon
8m/s²
Aishat
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
Saheed Reply
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
Ramon Reply
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
definitely of physics
Haryormhidey Reply
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Esrael Reply
what is field
Felix Reply
physics, biology and chemistry this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
WISDOM Reply
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
Belty Reply
a=v/t. a=f/m a
IHUMA
innocent
Adah
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
Nassze Reply
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
JALLAH Reply
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you. Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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