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# Gauss' Law

### Example Problems: Gauss' Law

A hollow, conducting sphere with an outer radius of 0.242m and an inner radius of 0.197m has a uniform surface charge density of 6.68*10^-6 C/m^2. A charge of -0.830 microC is now introduced into the cavity inside the sphere. A) What is the new charge density on the outside of the sphere in C/m^2? B) What is the strength of

### 1. the electric field just above the surface of the charged drum of photocopying machine has a magnitude E of 2.3X10^5 N/C. What is the surface charge density on the drum, assuming the drum is conductor? 2.A charge of uniform linear density 2.0nC/m is distributed along a long thin nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius=5.0cm, outer radius=10cm) The net charge on the shell is zero. (a)What is the magnitude of the electric field 15 cm from the axis of the shell? (b)What is the surface charge density on the inner and outer surface of the shell?

1. the electric field just above the surface of the charged drum of photocopying machine has a magnitude E of 2.3X10^5 N/C. What is the surface charge density on the drum, assuming the drum is conductor? 2.A charge of uniform linear density 2.0nC/m is distributed along a long thin nonconducting rod. The rod is coaxial with a

### Continuity of perpendicular component of the magnetic field

Maxwell's fourth equation states that div B = 0. Use this law to show that the component of B perpendicular to the surface is continuous (i.e., the same just below and just above the surface), regardless of the surface current Js(r, t).

### Concentric spheres

A metal sphere of radius a is surrounded by a metal shell of inner radius b and outer radius R, as shown in the diagram below. The flux through a spherical Gaussian surface located between a and b is 0.85Q/Eplison_o and the flux through a spherical Gaussian surface just outside R is 1.15Q/Eplison_o. What is the total charg

### A planar slab of thickness of 4.00 cm has a uniform volume charge density of 1.20×10-2 C/ m3. Find the magnitude of the electric field at all points in space both inside and outside the slab, in terms of x, the distance measured from the central plane of the slab. What is the field for x = 1.00 cm? What is the field for x = 8.00 cm?

A planar slab of thickness of 4.00 cm has a uniform volume charge density of 1.20×10-2 C/ m3. Find the magnitude of the electric field at all points in space both inside and outside the slab, in terms of x, the distance measured from the central plane of the slab. What is the field for x = 1.00 cm? What is the field for x = 8.0

### Electric field, Coulomb's and Gauss' law.

1. Can there be an electric field to the point where there is no charge? Can there be a charge at a place where there is no field? Please write a one or two sentence answer to each of these questions. 2. Let's say you are holding two tennis balls (one in each hand), and let's say that these balls each have a charge Q. estima

### Electrostatics: Field and force, Coulomb's law, Gauss law.

1. A system of 1525 particles, each of which is either an electron or a proton, has a net charge of -5.456 × 10-17C. (a) how many electrons are in this system? (b) What is the mass of this system? See attached file for full problem description. 2. See attached file for full problem description. 3. Three equal point c

### Finding Electric Fields

8. A sphere of radius R1 carries a uniform charge density p throughout its volume except for a small spherical hollow volume of radius R2 located at distance a from the center (and fully contained within the larger sphere). a) Calculate the electric field E at the center of the hollow sphere. [Be careful, you can't just ap

### Electric Fields using Gauss' Law

A hollow spherical shell carries charge density p = k / r^2, in the region a<=r<=b. Find the electric field in i) the region a< r< b.

### capacitors, voltage and resistance calculations

1) a. Show that the capacitance per unit length of a cylindrical capacitor is C'= (see attached), where R1 and R2 are the inner and outer radii. b. Calculate the capacitance per meter when R2/R1=e=2.718 2) Two capacitors C1 and C2 are charged to voltages V1 and V2 respectively and then connected to parallel, positive termi

### The Magnitude of the Electric Potential

A small charged sphere of radius a=1.10 cm is suspended by a nylon thread inside a larger neutral, conducting sphere. The larger sphere has an interior radius b=4.70 cm and is 0.5 cm thick. The charge on the small sphere is q=0.90 nC. The two spheres are concentric and insulated from their surroundings. For the following questio

### Electricity problems

1. Two spherical drops of mercury each have a charge of 0.1 nC and a potential of 300v at the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop? 2. A long thin straight wire with linear charge density (lambda) runs down the center of a thin, hollow metal cylinder of radiu

### Electrostatics: Field and Potential for Spherical Charges

In a conductor, all the charges must lie on the surfaces. In addition to the charge q on the inner sphere, note that induced positive and negative charges can strategically be distributed on the surfaces of the outer conduction shell. Which results in no net charge on the shell. See attached file for full problem description.

### Gaussian surface

Please help with the following problem. Step by step calculations are given. (See attached file for full problem description with proper symbols) A long straight conducting rod carries a linear charge density of +2.0 uC/m . This rod is totally enclosed within a thin cylindrical shell of radius R, which carries a linear c

### Potential Drop

Ten spherical mercury drops of equal size R carry the same charge Q each. They join into one big drop. Derive the expression for potential of this drop.

### Electrostatics: Field and Potential

Please solve and show solutions step by step for problems 22.38, 22.42, and 23.68 (See attached files for full problem description)

### Electric field inside the sphere using Gauss' law

Solid insulation sphere of non-uniform charge density. Finding the electric field in side the sphere using Gauss' law: (a) Consider a solid insulating sphere of radius b with non-uniform charge density s= ar, where 'a' is a constant. Find the charge Q_r contained within the radius r, when r < b. (b) If a = 2 x 10^-6 C

### Electric field for a given charge density.

(See attached file for full problem description) --- A plastic sheet of thickness t has a uniform free charge density, +&#61554;, embedded inside, and also one surface has a surface charge of -&#61555;. Find the electric field and the potential as functions of distance from one surface. [Please neglect the issues of dielec

### Electrostatics: Surface charge density and electric field

Two part question involving a spherical cavity inside a shell and calculating: a) the surface charge density b) the electric field Problem is attached in word format. Diagram is included in jpeg.

### Discussing Gauss's Law

A very long, insulating, cylinder with a radius of 1.0 cm has a uniform positive charge density of 1.0 C / m^3. (a) What is the magnitude of the electric field 0.5 cm from the center of the cylinder? (b) What is the magnitude of the electric field at the surface of the cylinder, i.e. 1.0 cm from the center of the cylinder? (c) W

### Electrical Field on a Gaussian Surface

The electrical field in a particular space is E = (X + 1.2)1 N/C with x in meters. Consider a cylindrical Gaussian surface of radius 16 cm that is coaxial with the x axis. One end of the cylinder is at x = 0. (a) What is the magnitude of the electric flux through the other end of the cylinder at x = 3.2 m? (b) What net charge is

### Gauss' law

A small nonconducting ball of mass m=1.0mg and charge q=2x10^-8C(distributed uniformly through its volume) hangs from an insulating thread that makes an angle of 30 degrees with a vertical, uniformly charged nonconducting sheet. Considering the gravitational force on the ball and assuming the sheet extends far vertically and in

### Spherical conducting shell, particle with a charge

Please show all work and show all equations used and diagrams. 1) A spherical conducting shell has charge Q. A particle with charge q is placed at the center of the cavity. The charge on the inner surface of the shell and the charge on the outer surface of the shell, respectively are: 2) A particle with a charge of 5.5*1

### Positive charge, magnitude of the electric field, charge is distributed uniformally

Please show all work and show all equations used and diagrams. 1) Positive charge Q is placed on a conducting sphereical shell with inner radius R1 and outer radius R2. A point charge q is placed at the center of the cavity. The magnitude of the electric field at a point outside the shell, a distance r from the center is:

### Finance and investment problem

PROBLEM OF (1) You are required to analyse each of the areas of statistics relating to business decision making explaining in detail what each of them do. . ? Descriptive Measures ? Probability ? Sampling Distributions ? Linear Regression ? Time Series Forecasting ? Index Numbers Decision Making (2

### Gauss' Lemma to show that 17 is a quadratic residue module 19.

6. Use Gauss' Lemma to show that 17 is a quadratic residue module 19. Please see attached.

### Gauss's Law Cylinder

See attachment for complete question and diagram. For points far from the ends of the cylinders, determine the electric field at the following radial distances from the central axis. (a) r = 2.0 cm (b) r = 6.0 cm (c) r = 13 cm

### Gauss's Law Spheres

A point charge of 3.40 nC is located at the origin and a second charge of -5.40 nC is located on the x axis at x = 1.50 m. Calculate the electric flux through a sphere centered at the origin with radius 1.00 m. Repeat the calculation for a sphere of radius 2.00 m.