The general form of Gauss's law describes how a charge cre-ates an electric field in a material, as well as in vacuum:TinE · dA =where e = Ke, is the permittivity of the material. (a) A sheetwith 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 oppositecharges of equal magnitude Q, are a small distance d apart.Show that they create uniform electric field in the spacebetween them with magnitude E = Q/Ae. (c) Assume thenegative plate is at zero potential. Show that the positiveplate is at potential Qd/Ae. (d) Show that the capacitance ofthe pair of plates is given by C = Ae/d = KA€,/d.

The given expression for the general form of the Gauss’s law, Using the general form of the…

Answered: The general form of Gauss's law…

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

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Chapter6: Gauss's Law

Section: Chapter Questions

Problem 64P: An aluminum spherical ball of radius 4 cm is charged with 5C of charge. A copper spherical shell of...

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The electric field 10.0 cm from the surface of a copper ball of radius 5.0 cm is directed toward the ball's center and has magnitude 4.0102 N/C. How much charge is on the surface of the ball?
Two parallel plates 10 cm on a side are given equal and opposite charges of magnitude 5109 C. The plates are 1.5 mm apart. What is the electric field at the center of the region between the plates?
A charge of 30C is distributed uniformly a spherical volume of radius 10.0 cm. Determine the electric field due to this charge at a distance of (a) 2.0 cm, (b) 5.0 cm, and (c) 20.0 cm from the center of the sphere.
On a typical clear day, the atmospheric electric field points downward and has a magnitude of approximately 100 N/C. Compare the gravitational and electric forces on a small dust particle of mass 2.01015 g that carries a single electron charge. What is the acceleration (both magnitude and direction) of the dust particle?
Determine if approximate cylindrical symmetry holds for the following situations. State why or why not. (a) A 300-cm long copper rod of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (b) A 10-cm long copper of radius 1 cm is charged with +500 nC of charge and we seek electric field at a point 5 cm from the center of the rod. (c) A 150-cm wooden rod is glued to a 150-cm plastic rod to make a 300 cm long rod, which is then painted with a charged paint so that one obtains a uniform charge density. The radius of each rod is 1 cm, and we seek an electric field at a point that is 4 cm from the center of the rod. (d) Same rod as (c), but we seek electric field at a point that is 500 cm from the center of the rod.
The surface charge density on a long straight metallic pipe is . What is the electric field outside and inside the pipe? Assume the pipe has a diameter of 2a.
What is the magnitude of the electric field just above the middle of a large, flat, horizontal sheet carrying a charge density of 98.0 nC/m2?
If more electric field lines leave a gaussian surface than enter it, what can you conclude about the net charge enclosed by that surface?
What is the magnitude of the electric field due to a charged particle at its exact location (r = 0)?
Two parallel conducting plates, each of cross-sectional area 400 cm2, are 2.0 cm apart and uncharged. If 1.01012 electrons are transferred from one plate to the other, what are (a) the charge density on each plate? (b) The electric field between the plates?
ne electric field at 2 cm from the center of long copper rod of radius 1 cm has a magnitude 3 N/C and directed outward from the axis of the rod. (a) How much charge per unit length exists on the rod? (b) What would be the electric flux through a cube of side 5 cm situated such that the rod passes through opposite sides of the cube perpendicularly?
A long copper cylindrical shell of inner radius 2 cm and outer radius 3 cm surrounds concentrically a charged long aluminum rod of radius 1 cm with a charge density of 4 pC/m. All charges on the aluminum rod reside at its surface. The inner surface of the copper shell has exactly charge to that of the aluminum rod while the outer surface of the copper shell has the same charge as the aluminum rod. Find the magnitude and direction of the electric field at points that are at the following distances from the center of the aluminum rod: (a) 0.5 cm, (b) 1.5 cm, (c) 2.5 cm, (d) 3.5 cm, and (e) 7 cm.

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