9/16/2015
MasteringPhysics: Ch 21 HW
The Trajectory of a Charge in an Electric Field An charge with mass m and charge q is emitted from the origin, (x, y) = (0, 0) . A large, flat screen is located at x = L . There is a target on the screen at y position y h , where y h > 0 . In this problem, you will examine two different ways that the charge might hit the target. Ignore gravity in this problem.
Part A Assume that the charge is emitted with velocity v 0 in the positive x direction. Between the origin and the screen, the charge travels through a constant electric field pointing in the positive y direction. What should the magnitude E of the electric field be if the charge is to hit the target on the screen? Express your answer in terms of m, q , yh , v 0 , and L.
Hint 1. How to approach the problem Once you determine the force on the charge due to the electric field, this becomes a standard two dimensional kinematics problem. To solve the problem, first determine the equations of motion in both the x and y directions. Then use the fact that at some final time tf inal you know that the position of the charge is (L, y ) to obtain two equations in terms of the two unknowns E and t f inal . Eliminate t f inal and solve for h E.
Hint 2. Find the equation of motion in the x direction Find an expression for x(t), the charge's x position as a function of time. Express your answer in terms of t as well as any of the given variables and constants.
Hint 1. Find the force in the x direction What net force Fx does the charge experience in the x direction?
Hint 1. Formula for the force on a charge in an electric field The formula for the force F ⃗ on a charge q in an electric field E⃗ is ⃗ ⃗ F = qE
.
ANSWER: Fx
= 0
Hint 2. A helpful kinematic equation Recall that kinematic equation that gives the distance s travelled in terms of the initial velocity u, the acceleration a and elapsed time t is s = ut +
1 2
at
2
.
ANSWER: https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120377&view=print&offset=next
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9/16/2015
MasteringPhysics: Ch 21 HW x(t)
=
v0 t
Hint 3. Find the equation of motion in the y direction Find an expression for y(t) , the charge's y position as a function of time. Express your answer in terms of t as well as any of the given variables and constants.
Hint 1. Find the force in the y direction What is the net force acting on the charge in the y direction? Express your answer in terms of the given variables and constants.
Hint 1. Formula for the force on a charge in an electric field The formula for the force F ⃗ on a charge q in an electric field E⃗ is ⃗ ⃗ F = qE
.
ANSWER: Fy
=
qE
Hint 2. A helpful kinematic equation Recall that kinematic equation that gives the distance s travelled in terms of the initial velocity u, the acceleration a and elapsed time t is s = ut +
1 2
at
2
.
ANSWER: y(t)
=
1
qE
2
m
t
2
Hint 4. Combine Your Results At some final time tf inal , you have x(tf inal ) eliminate tf inal and solve for E .
= L
and y(tf inal )
= y
h
. Starting with these two equations,
Hint 5. Find t f inal Use the equation for the motion of the charge in the x direction to find tf inal . Express your answer in terms of the variables v 0 and L. ANSWER: https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120377&view=print&offset=next
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9/16/2015
MasteringPhysics: Ch 21 HW
t f inal
L
=
v0
ANSWER: 2my h
E
=
2
q(
L v
)
0
Correct
Part B Now assume that the charge is emitted with velocity v 0 in the positive y direction. Between the origin and the screen, the charge travels through a constant electric field pointing in the positive x direction. What should the magnitude E of the electric field be if the charge is to hit the target on the screen? Express your answer in terms of m, q , yh , v 0 , and L.
Hint 1. How to approach the problem Just as in the previous part, once you determine the force on the charge due to the electric field, this becomes a standard twodimensional kinematics problem. To solve the problem, first determine the equations of motion in both the x and y directions. Then use the fact that at some final time tf inal you know that the position of the charge is (L, yh ) to obtain two equations in terms of the two unknowns E and t f inal . Eliminate t f inal and solve for E .
Hint 2. Find the equation of motion in the y direction Find an expression for y(t) , the charge's y position as a function of time. Express your answer in terms of t as well as any of the given variables and constants.
Hint 1. Find the force in the y direction What net force Fy does the charge experience in the y direction?
Hint 1. Formula for the force on a charge in an electric field The formula for the force F ⃗ on a charge q in an electric field E⃗ is ⃗ ⃗ F = qE
.
ANSWER: Fy
= 0
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120377&view=print&offset=next
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9/16/2015
MasteringPhysics: Ch 21 HW
Hint 2. A helpful kinematic equation Recall that kinematic equation that gives the distance s travelled in terms of the initial velocity u, the acceleration a and elapsed time t is s = ut +
1 2
at
2
.
ANSWER: y(t)
=
v0 t
Hint 3. Find the equation of motion in the x direction Find an expression for x(t), the charge's x position as a function of time. Express your answer in terms of t as well as any of the given variables and constants.
Hint 1. Find the force in the x direction What is the net force acting on the charge in the x direction? Express your answer in terms of the given variables and constants.
Hint 1. Formula for the force on a charge in an electric field The formula for the force F ⃗ on a charge q in an electric field E⃗ is ⃗ ⃗ F = qE
.
ANSWER: Fx
=
qE
Hint 2. A helpful kinematic equation Recall that kinematic equation that gives the distance s travelled in terms of the initial velocity u, the acceleration a and elapsed time t is s = ut +
1 2
at
2
.
ANSWER: x(t)
=
1
qE
2
m
t
2
Hint 4. Combine your results ( ) = ( ) = https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120377&view=print&offset=next
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9/16/2015
MasteringPhysics: Ch 21 HW
At some final time tf inal , you have x(tf inal ) eliminate tf inal and solve for E .
= L
and y(tf inal )
= y
h
. Starting with these two equations,
Hint 5. Find t f inal Use the equation for the motion of the charge in the y direction to find tf inal . Express your answer in terms of the variables v 0 and yh . ANSWER: t f inal
y
=
h
v0
ANSWER: 2mL
E
=
2 y
q(
h
v
)
0
Correct The equations of motion for this part are identical to the equations of motion for the previous part, with L and y h interchanged. Thus it is no surprise that the answers to the two parts are also identical, with L and y h interchanged.
https://session.masteringphysics.com/myct/itemView?assignmentProblemID=54120377&view=print&offset=next
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