Describe a force field and calculate the strength of an electric field due to a point charge.
Calculate the force exerted on a test charge by an electric field.
Explain the relationship between electrical force (
F ) on a test charge and electrical field strength (
E ).
The information presented in this section supports the following AP® learning objectives and science practices:
2.C.1.1 The student is able to predict the direction and the magnitude of the force exerted on an object with an electric charge
q placed in an electric field
E using the mathematical model of the relation between an electric force and an electric field:
, a vector relation.
(S.P. 2.2)
2.C.1.2 The student is able to calculate any one of the variables – electric force, electric charge, and electric field – at a point given the values and sign or direction of the other two quantities.
(S.P. 2.2)
2.C.2.1 The student is able to qualitatively and semiquantitatively apply the vector relationship between the electric field and the net electric charge creating that field.
(S.P. 2.2, 6.4)
3.C.4.1 The student is able to make claims about various contact forces between objects based on the microscopic cause of those forces.
(S.P. 6.1)
3.C.4.2 The student is able to explain contact forces (tension, friction, normal, buoyant, spring) as arising from interatomic electric forces and that they therefore have certain directions.
(S.P. 6.2)
Contact forces, such as between a baseball and a bat, are explained on the small scale by the interaction of the charges in atoms and molecules in close proximity. They interact through forces that include the
Coulomb force . Action at a distance is a force between objects that are not close enough for their atoms to “touch.” That is, they are separated by more than a few atomic diameters.
For example, a charged rubber comb attracts neutral bits of paper from a distance via the Coulomb force. It is very useful to think of an object being surrounded in space by a
force field . The force field carries the force to another object (called a test object) some distance away.
Concept of a field
A field is a way of conceptualizing and mapping the force that surrounds any object and acts on another object at a distance without apparent physical connection. For example, the gravitational field surrounding the earth (and all other masses) represents the gravitational force that would be experienced if another mass were placed at a given point within the field.
In the same way, the Coulomb force field surrounding any charge extends throughout space. Using Coulomb's law,
, its magnitude is given by the equation
, for a
point charge (a particle having a charge
) acting on a
test charge
at a distance
(see
[link] ). Both the magnitude and direction of the Coulomb force field depend on
and the test charge
.
The Coulomb force field due to a positive charge
is shown acting on two different charges. Both charges are the same distance from
. (a) Since
is positive, the force
acting on it is repulsive. (b) The charge
is negative and greater in magnitude than
, and so the force
acting on it is attractive and stronger than
. The Coulomb force field is thus not unique at any point in space, because it depends on the test charges
and
as well as the charge
.
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?
