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Imagine two parallel infinite sheets, carrying uniform
Chapter 8, Problem 5P(choose chapter or problem)
Problem 5P
Imagine two parallel infinite sheets, carrying uniform surface charge +σ (on the sheet at z = d) and −σ (at z = 0). They are moving in the y direction at constant speed v (as in Problem 5.17).
(a) What is the electromagnetic momentum in a region of area A?
(b) Now suppose the top sheet moves slowly down (speed u) until it reaches the bottom sheet, so the fields disappear. By calculating the total force on the charge (q = σ A), show that the impulse delivered to the sheet is equal to the momentum originally stored in the fields. [Hint: As the upper plate passes by, the magnetic field drops to zero, inducing an electric field that delivers an impulse to the lower plate.]
reference prob 5.17
A large parallel-plate capacitor with uniform surface charge σ on the upper plate and −σ on the lower is moving with a constant speed v, as shown in
Fig. 5.43.
(a) Find the magnetic field between the plates and also above and below them.
(b) Find the magnetic force per unit area on the upper plate, including its direction.
(c) At what speed v would the magnetic force balance the electrical force?15
Fig. 5.43.
Questions & Answers
QUESTION:
Problem 5P
Imagine two parallel infinite sheets, carrying uniform surface charge +σ (on the sheet at z = d) and −σ (at z = 0). They are moving in the y direction at constant speed v (as in Problem 5.17).
(a) What is the electromagnetic momentum in a region of area A?
(b) Now suppose the top sheet moves slowly down (speed u) until it reaches the bottom sheet, so the fields disappear. By calculating the total force on the charge (q = σ A), show that the impulse delivered to the sheet is equal to the momentum originally stored in the fields. [Hint: As the upper plate passes by, the magnetic field drops to zero, inducing an electric field that delivers an impulse to the lower plate.]
reference prob 5.17
A large parallel-plate capacitor with uniform surface charge σ on the upper plate and −σ on the lower is moving with a constant speed v, as shown in
Fig. 5.43.
(a) Find the magnetic field between the plates and also above and below them.
(b) Find the magnetic force per unit area on the upper plate, including its direction.
(c) At what speed v would the magnetic force balance the electrical force?15
Fig. 5.43.
ANSWER:
Solution 5P
Step 1 of 6:
In part (a), our aim is to find the electromagnetic momentum in a region of area A in between the two parallel infinite sheets moving in the y direction at constant speed v.