Magnetic fields exert forces on moving charges. This force is one of the most basic known. The direction of the magnetic force on a moving charge is perpendicular to the plane formed by
and
and follows right hand rule–1 (RHR-1) as shown. The magnitude of the force is proportional to
,
,
, and the sine of the angle between
and
.
Making connections: charges and magnets
There is no magnetic force on static charges. However, there is a magnetic force on moving charges. When charges are stationary, their electric fields do not affect magnets. But, when charges move, they produce magnetic fields that exert forces on other magnets. When there is relative motion, a connection between electric and magnetic fields emerges—each affects the other.
Calculating magnetic force: earth’s magnetic field on a charged glass rod
With the exception of compasses, you seldom see or personally experience forces due to the Earth’s small magnetic field. To illustrate this, suppose that in a physics lab you rub a glass rod with silk, placing a 20-nC positive charge on it. Calculate the force on the rod due to the Earth’s magnetic field, if you throw it with a horizontal velocity of 10 m/s due west in a place where the Earth’s field is due north parallel to the ground. (The direction of the force is determined with right hand rule 1 as shown in
[link] .)
A positively charged object moving due west in a region where the Earth’s magnetic field is due north experiences a force that is straight down as shown. A negative charge moving in the same direction would feel a force straight up.
Strategy
We are given the charge, its velocity, and the magnetic field strength and direction. We can thus use the equation
to find the force.
Solution
The magnetic force is
We see that
, since the angle between the velocity and the direction of the field is
. Entering the other given quantities yields
Discussion
This force is completely negligible on any macroscopic object, consistent with experience. (It is calculated to only one digit, since the Earth’s field varies with location and is given to only one digit.) The Earth’s magnetic field, however, does produce very important effects, particularly on submicroscopic particles. Some of these are explored in
Force on a Moving Charge in a Magnetic Field: Examples and Applications .
A proton moves in the –
x -direction and encounters a uniform magnetic field pointing in the +
x -direction. In what direction is the resulting magnetic force on the proton?
A proton moves with a speed of 240 m/s in the +
x -direction into a region of a 4.5-T uniform magnetic field directed 62° above the +
x -direction in the
x ,
y -plane. Calculate the magnitude of the magnetic force on the proton.
Magnetic fields exert a force on a moving charge
q , the magnitude of which is
where
is the angle between the directions of
and
.
The SI unit for magnetic field strength
is the tesla (T), which is related to other units by
The
direction of the force on a moving charge is given by right hand rule 1 (RHR-1): Point the thumb of the right hand in the direction of
, the fingers in the direction of
, and a perpendicular to the palm points in the direction of
.
The force is perpendicular to the plane formed by
and
. Since the force is zero if
is parallel to
, charged particles often follow magnetic field lines rather than cross them.
Conceptual questions
If a charged particle moves in a straight line through some region of space, can you say that the magnetic field in that region is necessarily zero?
What is the direction of the velocity of a negative charge that experiences the magnetic force shown in each of the three cases in
[link] , assuming it moves perpendicular to
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 in the figure below, assuming
is perpendicular to
?
What is the maximum force on an aluminum rod with a
charge that you pass between the poles of a 1.50-T permanent magnet at a speed of 5.00 m/s? In what direction is the force?
perpendicular to both the magnetic field lines and the velocity
(a) Aircraft sometimes acquire small static charges. Suppose a supersonic jet has a
charge and flies due west at a speed of 660 m/s over the Earth’s south magnetic pole, where the
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) A cosmic ray proton moving toward the Earth at
experiences a magnetic force of
. What is the strength of the magnetic field if there is a
angle between it and the proton’s velocity? (b) Is the value obtained in part (a) consistent with the known strength of the Earth’s magnetic field on its surface? Discuss.
(a)
(b) This is slightly less then the magnetic field strength of
at the surface of the Earth, so it is consistent.
An electron moving at
in a 1.25-T magnetic field experiences a magnetic force of
. What angle does the velocity of the electron make with the magnetic field? There are two answers.
(a) A physicist performing a sensitive measurement wants to limit the magnetic force on a moving charge in her equipment to less than
. What is the greatest the charge can be if it moves at a maximum speed of 30.0 m/s in the 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.
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.
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?
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
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
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
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
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?
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?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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