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.
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?
