The general form of Gauss's law describes how a charge cre- ates an electric field in a material, as well as in vacuum: Tin E · dA = where e = Ke, is the permittivity of the material. (a) A sheet with charge Q uniformly distributed over its area A is sur- rounded by a dielectric. Show that the sheet creates a uni- form electric field at nearby points with magnitude E = Q/2 Ae. (b) Two large sheets of area A, carrying opposite charges of equal magnitude Q, are a small distance d apart. Show that they create uniform electric field in the space between them with magnitude E = Q/Ae. (c) Assume the negative plate is at zero potential. Show that the positive plate is at potential Qd/Ae. (d) Show that the capacitance of the pair of plates is given by C = Ae/d = KA€,/d.

The general form of Gauss's law describes how a charge cre- ates an electric field in a material, as well as in vacuum: Tin E · dA = where e = Ke, is the permittivity of the material. (a) A sheet with charge Q uniformly distributed over its area A is sur- rounded by a dielectric. Show that the sheet creates a uni- form electric field at nearby points with magnitude E = Q/2 Ae. (b) Two large sheets of area A, carrying opposite charges of equal magnitude Q, are a small distance d apart. Show that they create uniform electric field in the space between them with magnitude E = Q/Ae. (c) Assume the negative plate is at zero potential. Show that the positive plate is at potential Qd/Ae. (d) Show that the capacitance of the pair of plates is given by C = Ae/d = KA€,/d.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: The equation E = 1 qd is approximation of the magnitude of the electric field of an electric dipole,…

A: Solution:-Given thatz=17dEappr=12πεoqdz3

Q: a certain region of space, the electric field E is uniform. (a) Use Gauss's law to ove that this…

Q: A spherical capacitor consists of two concentric spheres with the inner sphere of radius a and the…

A: Gauss's law: It states that the electric flux (ϕ) through any closed surface is proportional to the…

Q: Their are two thin circular rings of radius R and charge -Q with their axes coinciding. One of the…

A: The magnitude of electric field due to a point charge q can expressed by the following relation.…

Q: Consider the following figure. (If you need to use es or -, enter INFINITY or -INFINITY,…

A: To calculate the total electric field at x=1.00 cm, the total electric field at x=12.70 cm and the…

Q: The electric field in a certain region of Earth's atmosphere is directed vertically down. At an…

A: Given, The electric field in a certain region of Earth's atmosphere is directed vertically down. At…

Q: Consider a thin-shelled hollow tube of length L, radius R with a uniform surface charge of density ?…

Q: Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an…

A: Given, The radius of disk=R In figure a, z=5.10R In figure b, R'=R5.10 Let the surface charge…

Q: An infinite line of charge produces a field of magnitude 4.0 × 104 N/C at a distance of 2.3 m.…

Q: A small sphere of mass m carries a charge of q. It hangs from a silk thread which makes an angle…

A: Given that, A small sphere of mass m carries a charge of q. It hangs from a silk thread which makes…

Q: It is found experimentally that the electric field in a certain region of Earth's atmosphere is…

A: This question is based on Gauss law.

Q: (a) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown…

A: Given data *The Given charges are q1=6.00 μC=6.00×10-6 Cq2=1.50 μC=1.50×10-6 Cq3=-2.00…

Q: spherical mass of 500 g is in an electric field of 10N/C directly vertically upward. How much charge…

A: Mass = m = 500g = 0.5 kg Electric field = E = 10 N/C Charge = q = ?

Q: An insulating sphere with an 3 cm radius has a uniform charge of 12 µC. What is the magnitude ofthe…

A: Step 1:Radius is 3cm is 0.03mCharge is 12μCDistance is 2cm is 0.02mStep 2:The formula for magnitude…

Question

The general form of Gauss's law describes how a charge cre-
ates an electric field in a material, as well as in vacuum:
Tin
E · dA =
where e = Ke, is the permittivity of the material. (a) A sheet
with charge Q uniformly distributed over its area A is sur-
rounded by a dielectric. Show that the sheet creates a uni-
form electric field at nearby points with magnitude E =
Q/2 Ae. (b) Two large sheets of area A, carrying opposite
charges of equal magnitude Q, are a small distance d apart.
Show that they create uniform electric field in the space
between them with magnitude E = Q/Ae. (c) Assume the
negative plate is at zero potential. Show that the positive
plate is at potential Qd/Ae. (d) Show that the capacitance of
the pair of plates is given by C = Ae/d = KA€,/d.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Part (a)

Part (b)

Part (c)

Part (d)

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A point charge q= 4.7 uC is placed at each corner of an equilateral triangle with sides 210mm in length. (a) What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle? b) is the magnitude of the elctric field at the ceneter of the triangle less than, greater than or the same as the magnitufr at midpoint of a side? Draw a skwtch with all apprpoate vectors.
Suppose a point charge creates a 10500 N/C electric field at a distance of 0.55 m. The magnitude of the point charge in coloumbs in 3.53x10-7. What is the strength of the field, in ntewtons per coulomb, at a distance of 10 m?
Asap plzzz
using Gauss’s Law please find the electric field due to an infinite line of charge with constant charge density λ Coloumbs per metre. Also why it is important that the line of charge is infinite?
(a) Determine the electric field strength at a point 1.00 cm to the left of the middle charge shown in the figure below. (Enter the magnitude of the electric field only.) (b) If a charge of −6.49 µC is placed at this point, what are the magnitude and direction of the force on it?