Gauss' law Definition and 341 Threads

Homework Statement I actually just have two questions about the law itself. 1.) Is Gauss's Law just the projection of a shape onto a perpindicular surface to the E field,times the E field? I ask this because there is an example in my book which shows a 3D incline with a horizontal E...

Homework Statement A square plate of copper with 50.0-cm sides has no net charge and is placed in a region of uniform electric field of 80.0 kN/C directed perpendicularly to the plate. Find: (a) the charge density of each face of the plate and (b) the total charge on each face Homework...

Gauss' Law only figures out the the total charge enclosed by the Gaussian surface and on it, I treid this in a few cases where charges were placed only inside the surface, and my answers were correct. But, when I tried imagining how to do this if there were charges present outside...

Homework Statement A point charge Q is located at the origin. The point charge produces an electric field at a radius of 2.0 meters from the origin of 20N/c.The electric potential of a spherical surface of radius 3.0 meters around the point charge is, in Volts. Homework Equations...

Hi I'm just making sure I'm understanding the information I'm getting from "A Student's Guide to Maxwell's Equations" The book is talking about Gauss' Law for Electric Fields \bold{E\cdot n}\;\; = E cos (90) = 0 Does this mean that the full electric field is going through the...

Homework Statement Prove \nabla \bullet E =4 \pi \rho from \partial_{\beta}F^{\alpha \beta}=4 \pi J^{\alpha} where J^{\alpha}=(\rho, J^{1}, J^{2}, J^{3}). Homework Equations We are given that F_{\alpha \beta} is 0~~~~E_x~~~E_y~~~E_z -E_x~~~0~~~~-B_z~~B_y -E_y~~B_z~~~~0~~~-B_x...

Homework Statement Non conducting solid cube with a uniform charge distribution. Why is it impossible, or extremely difficult to calculate the field using a larger cube as the gaussian, what about with a sphere as the gaussian? Homework Equations gauss' law The Attempt at a...

Homework Statement Figure 23-30 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 µC/m2 on its outer surface and radius 3.0 cm. Shell 2 has uniform surface charge density -3.8 µC/m2 on its outer surface and radius 2.0 cm. The shell centers...

An infinite line charge lies on the z-axis with l = 2 µC/m. Coxaial with that line charge are: an infinite conducting shell (with no net charge) with thickness 1 cm and with inner radius 2 cm and outer radius 3 cm, an infinite shell with a radius of 4 cm and with a net charge of -5 µC/m, and...

An infinite line charge lies on the z-axis with l = 2 µC/m. Coxaial with that line charge are: an infinite conducting shell (with no net charge) with thickness 1 cm and with inner radius 2 cm and outer radius 3 cm, an infinite shell with a radius of 4 cm and with a net charge of -5 µC/m, and...

An infinite line charge lies on the z-axis with l = 2 µC/m. Coxaial with that line charge are: an infinite conducting shell (with no net charge) with thickness 1 cm and with inner radius 2 cm and outer radius 3 cm, an infinite shell with a radius of 4 cm and with a net charge of -5 µC/m, and...

I'm reading the book "Electricity and Magnetism: Vol. II" by Edward M. Purcell, in which he describes Gauss' law as stating that the flux through a closed surface is 4π times the enclosed charge (he uses the Centimeter-Gram-Second system). Later, he refers to Gauss' law as stating that the...

Here's the good explanation. ---------- A surface is an abstract mathematical tool that we can use to explore various phenomena. What a surface is, is a shell around a region of space. Consider a common inflatable ball, such as a soccer ball, or a basketball. The "ball" itself is just a...

I need an explanation that relates the equation to what I learned about the dot product of two vectors being the magnitude of the parallelogram formed by the two vectors in 2D or similarly by the paralleliped formed by three vectors in 3D. I want to know for instance if the resultant is...

Homework Statement A long, thin, straight wire of length L has a positive charge Q distributed uniformly along it. Use Gauss' Law to show that the electric field created by this wire at a radial distance r has a magnitude of E = λ/(2πεor), where λ = Q/L. (Hint: For a Gaussian surface, use a...

Homework Statement A linear charge lambda = 10^-11 C/m is uniformly distributed along a thin nonconductive rod of length L = 0.5 m. Use Gauss' Law to calculate the field at a distance of r = 0.1 m from the charged rod. Homework Equations ∮E.da = Q/ε_0 The Attempt at a Solution Hi...

Homework Statement A 2 C charge is spread uniformly in a hollow sphere with a radius of 50 cm. a) What is the electric flux? b) What is the magnitude and direction of an electric field 200 cm away? Homework Equations Electric flux = q/(permittivity of free space) E = q/4(pi)(permittivity...

Hi All, I am studying Gauss' law and have learned that using symmetry, we need to select a cyclinder in order to calculate electric field of an infinite plane sheet of charge. 2EA = \frac {\sigma A} {\epsilon} That equation is written using Gauss' law and hence E field is found...

Homework Statement A sphere has outer radius 15 and inner radius 5. Between r= 5 and 15, the sphere is solid and contains a total charge of 20 C. At r < 5, the sphere is hollow. Calculate the electric field at r = 8. Homework Equations Gauss' Law --> EA = (q)/epsilon zero...

Use Gauss' Law to find the electric field, everywhere,of charge of uniform density \rho occupying the region a<r<b, where r is the distance from the origin. Having done this, find the potential. Ok, so far I said that by Gauss' Law, \Phi=\oint_S \vec{E} \cdot \vec{dS} = \int_V \nabla \cdot...

Homework Statement I just have a little question about Gauss' Law (differential form). If divE = p/e0 where p is the charge density and e0 is permittivity of free space. But if we had a sphere with a total net charge of Q, then outside the sphere, the field is E=k/r^2 I think. Then...

Hello, Thank you very much for takign the time to help me out. This is an applied calculus 3 (multivariable calc) level problem. I have an answer, but it is nonsensical as the units are not in accordance with units of charge, C. Homework Statement Instructions: Use Gauss' Law for...

Homework Statement A very long, solid insulating cylinder with radius R has a cylindrical hole with radius a bored along its entire length. The axis of the hole is a distance b from the axis of the cylinder, where a < b < R. The solid material has a uniform volume charge density, ρ. Find...

Gauss' Law - Sphere with spherical cavity - Please help Homework Statement A sphere of radius 2a is made of nonconducting material that has a uniform volume charge density . (Assume that the material does not affect the electric field.) A spherical cavity of radius a is now removed from the...

Say we are looking at a positively charged rod with uniform charge density and a radius of R. When using Gauss' law and taking a cylindrical surface we use the formula E = lambda/2*pi*epsilon*r When we derive this equation we are assuming R is significantly smaller than L and so we...

A long non-conducting cylinder has a charge density p = a*r, where a = 4.73 C/m^4 and r is in meters, and a radius of 0.0437m . Concentric around it is a hollow metallic cylindrical shell with an inner radius of 0.119m and an outer radius of 0.158m. 1) What is the electric field at 0.172m...

Two large flat metal sheets are a distance L apart. The separation L is small compared to the lateral dimensions of the sheets. Each sheet has a total surface area A, which includes both top and bottom surfaces of the sheet. The thickness of each sheet is very small compared to its lateral...

Can someone explain the following? A positive charge Q is placed on a square sheet of nonconducting material of side x cm in the yz plane. What's the magnitude and direction of the electric field next to the sheet and proximate to the center of the sheet? I don't understand why the...

Homework Statement Two nonconducting spheres, of r1=3.0cm and r2=2.0cm, are placed of an x-axis. They have surface charge densities of +6.0mC/m2 and +4.0 mC/m2, respectively, on their outside surfaces. The center of sphere r1 is on the origin and the center of sphere r2 is 10 cm away. What is...

The earth’s electric field is measured at a height of 200 m and is found to be directed vertically downwards and to have a strength of 100 Vm1. At a height of 300 m, the direction of the field is found to be the same, but the field’s strength has decreased to 60 Vm1. Use Gauss’ law to...

hello, I was wondering if there is an equivalent gauss' law for gravitation like: \Phi=4\piG*Menclosed any help would be appreciated. Thank you.

I really just want to know if I'm doing this correctly, as I don't have access to the answer to check. Homework Statement A cylindrical shell of radius 7.00 cm and length 240 cm has its charge uniformly distributed on its curved surface. The magnitude of the electric field at a point 19.0 cm...

Consider an insulating sphere with radius of 7 cm. A charge of 13.8561 µC is uniformly distributed throughout this sphere. It is surrounded by a conducting shell. Denote the charge on the inner surface of the shell to be q2 and the charge on the outer surface of the shell to be q3. The total...

A long non-conducting cylinder has a charge density ρ = α*r, where α = 4.95 C/m4 and r is in meters. Concentric around it is a hollow metallic cylindrical shell. https://www.physicsforums.com/attachment.php?attachmentid=14741&d=1216404841 1. What is the electric field at 2 cm from the...

Homework Statement a small circular hole of radius R = 2.03 cm has been cut in the middle of an infinite, flat, nonconducting surface that has a uniform charge density σ = 4.61 pC/m^2. A z axis, with its origin at the hole's center, is perpendicular to the surface. What is the magnitude (in...

Homework Statement A charge of uniform linear density 2.80 nC/m is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell (inner radius = 5.20 cm, outer radius = 10.8 cm). The net charge on the shell is zero. (a) What is the magnitude...

Homework Statement The box-like Gaussian surface of the figure below encloses a net charge of +57.0ε0 C and lies in an electric field given by = [(10.3 + 2.4x)·i - 3.1·j + bz·k ] N/C, with x and z in meters and b a constant. The bottom face is in the xz plane; the top face is in the...

http://imageupload.com/out.php/i120384_Untitled.gif I havnt had any luck with this question. The only possible approach i can think of is to use gauss' law for electric fields. I know I am supposed to show my working, but this really had me stumped, and I've really gotten nowhere. I...

Can anyone explain this to me?

Homework Statement In a spherical region, the voltage is measured to be spherically symmetrical, with v=v(r)=wr^p a. Find the radial electric field. b. Use Gauss’ Law to find the charge enclosed in a sphere of radius r. c. Find the charge enclosed by a sphere of radius...

1 A solid metal sphere of radius R has charge +2Q. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge -Q. a) Describe the electric field lines both inside and outside the spheres. b) Use Gauss' law to find an expression for the magnitude of the...

Homework Statement A solid sphere contains a uniform volume charge density (charge Q, radius R). (a) Use Gauss’s law to find the electric field inside the sphere. (b) Integrate E^2 over spherical shells over the volumes inside and outside the sphere. (c) What fraction of the total electrostatic...

! AHH Gauss' Law! Homework Statement Figure 23-27 is a section of a conducting rod of radius R1 = 1.30 mm and length L = 11.00 m inside a thick-walled coaxial conducting cylindrical shell of radius R2 = 10.0R1 and the (same) length L. The net charge on the rod is Q1 = +3.40 × 10^-12 C; that...

the electric field produced due to a time varying magnetic field is non-conservative in nature. does it follow gauss law?

I'm still not confident with these kinds of problems. Hopefully I got it right, but can someone double check my work? Thanks! Two parallel, infinite planes are separated by a distance d. Find the electric field everywhere (a) if both planes carry a surface charge density \sigma and (b)...

Homework Statement If the electric field of a point charge were proportional to 1/(r^3) instead of 1/(r^2), would Gauss's law still be valid? Explain reasoning. Homework Equations The Attempt at a Solution Considered a spherical Gaussian surface centered on a single point charge.

Homework Statement A certain region of space bounded by an imaginary closed surface contains no charge. Is the electric field always zero on the surface? If not, under what circumstances is it zero on the surface? Homework Equations Φ = Qenclosed÷εo = EA The Attempt at a Solution...

[SOLVED] Gauss' Law With an Infinite Cylinder of Charge Homework Statement The test question was to find the potential difference between a point S above a cylinder of charger per length lambda, and a point on the surface of the cylinder having radius R and infinite length. Homework...

Homework Statement An insulator in the shape of a spherical shell is shown in cross-section above. (see attached .gif) The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = + 9 mC (1 mC = 10-6 C). (You may assume that the charge...

Homework Statement A point charge q_{1} = 4.15 \times 10^-6 is located on the x-axis at x = 1.80 m, and a second point charge q_{2} = -5.80 \times 10^-6 C is on the y-axis at y = 1.10 m. What is the total electric flux due to these two point charges through a spherical surface centered at...