# gauss law

1. ### Electric Flux through a circle

Hi! My main problem is that I don't understand what the problem is telling me. What does it mean that the surface is a flast disc bounded by the circle? Is the Gauss surface the disc? Does that mean that inside the circle in the figure, there is a disc? Can you give me some guidance on how to...
2. ### Find the Electric Field E using Gauss' Law

I tried to work out both a) and b), but I am not sure if I am correct. I drew a picture with a sphere around q first with radius r and then with radius 3r. For a) $E.A=\frac {q}{ε_°}$ (when using Gauss' Law) Since $A=4πr^2$, I substituted this in the equation and solved for E giving me...
3. ### B Doubt on an EM problem regarding gauss law

There's this problem 2.18 in the book "Introduction to electrodynamics" by Griffith. The problem says the following, "Two spheres, each of radius R and carrying uniform charge densities $+\rho$ and $-\rho$, respectively, are placed so that they partially overlap (Image_01). Call the vector...
4. ### Potential across a conducting sphere surrounded by an insulator

1. Homework Statement A conducting sphere has a radius of 2.25 m and carries a positive surplus charge of 35.0 mC. A protective layer of barium titanate is applied to the surface of the sphere to make it safe for laboratory workers nearby. Safety considerations dictate that the potential...
5. ### Flux linked with lower face of a cube

1. Homework Statement A point charge q is placed inside a cube of side 2a. What will be the flux associated with the lower surface ABCD? 2. Homework Equations I think I can apply Gauss Law here, but can't think of something connecting it with the lower surface. ∫B.dl = 1/ε° X Charge Enclosed...
6. ### Find the electric field at an arbitrary point

1. Homework Statement A distribution of charge with spherical symmetry has volumetric density given by: $$\rho(r) = \rho_0 e^{ \frac {-r} {a} }, \left( 0 \leq r < \infty \right);$$ where $\rho_0$ and $a$ is constant. a) Find the total charge b) Find $\vec E$ in an arbitrary point 2...
7. ### Gauss' Law problem: determine the electric flow through a square surface due to a nearby charge

1. Homework Statement determine the electric flow through a square surface of side 2l due to a load + Q located at a perpendicular distance l from the center of the plane I really don't know how to answer this question .i need help guys Thanks 2. Homework Equations 3. The Attempt at a...
8. ### Flux of a vector and parametric equation

1. Homework Statement Compute the flux of a vector field $\vec{v}$ through the unit sphere, where $$\vec{v} = 3xy i + x z^2 j + y^3 k$$ 2. Homework Equations Gauss Law: $$\int (\nabla \cdot \vec{B}) dV = \int \vec{B} \cdot d\vec{a}$$ 3. The Attempt at a Solution Ok so after applying...
9. ### Electric Flux through the Face of a Cube

1. Homework Statement Griffiths' Introduction to Electrodynamics problem 2.10, 2. Homework Equations Gauss' Law, $\int_{S} \textbf{E}\cdot \textbf{dS} = \frac{Q_{\text{enc}}}{\epsilon_0}$ 3. The Attempt at a Solution It seems reasonable that the flux through the shaded surface and...
10. ### B Finding electric flux using Gauss' Law

Say you have a hollow cylinder, whose one side is open. Now, you pace a positive charge $Q$ at the centre of this open end (such that it is just inside the cylinder). How much should be the flux coming out from the closed end? I just thought of this problem. In order to use Gauss' Law, we...
11. ### Capacitance of a sphere

1. Homework Statement Assume a conducting sphere has a radius of 3400km with an electric field of 100 V/m at it's surface. a) Calculate total charge of sphere. b)Calculate potential at the surface using infinity at reference point c) Calculate capacitance of the sphere using the result of a or...
12. ### Gauss Law- Conducting and Non-conducting cylindrical shells

1. Homework Statement Below is a diagram of an infinitely long non-conducting rod of radius, R, with a uniform continuous charge distribution. The uniform linear charge density of this line is lamba1. The rod is at the center of an infinitely long, conducting pipe. The linear charge density of...
13. ### Electric field inside/outside (uniformly charged sphere)

A sphere of radius a carries a total charge q which is uniformly distributed over the volume of the sphere. I'm trying to find the electric field distribution both inside and outside the sphere using Gauss Law. We know that on the closed gaussian surface with spherically symmetric charge...
14. ### Classical Book(s) with problems on classical electromagnetism

I started studying the book "A Student's Guide to Maxwell's Equations" by Daniel Fleisch some time back. It is an excellent book, giving a very good idea about the main laws of electromagnetism. I will soon finish the book. Now I need some book(s) which has problems on all the laws in classical...
15. ### Electrostatic force between a Half Cylinder and a Plate

1. Homework Statement (This is not a HW problem, but HW-type problem.) A half cylinder of radius R and length L>>R is formed by cutting a cylindrical pipe made of an insulating material along a plane containing its axis. The rectangular base of the half cylinder is closed by a dielectric plate...
16. ### Finding the gravitational force over a flat infinite sheet

1. Homework Statement 2. Homework Equations F=ma F=Gm1m2/r2 Gauss' Law? 3. The Attempt at a Solution I'm not sure if I should be using Gauss' Law for this question, because I've never heard of it or learned about it. I'm currently taking multi-variable calculus (gradients, vectors, etc.)...
17. ### Application of Gauss' Law

1. Homework Statement Question ==== An infinitely long insulating cylindrical rod with a positive charge $\lambda$ per unit length and of radius $R_1$ is surrounded by a thin conducting cylindrical shell (which is also infinitely long) with a charge per unit length of $-2\lambda$ and...
18. ### Electric Field of a solid sphere of non-uniform surface density

A solid sphere has surface charge density, Rho (r) Rho(r) = k 1 ( 0 < r < a) k2 x ( a < r < R) 2) Find the electric field in all region i.e 1) r < a and 2) a < r < R and 3 ) R < The attempted solution and the question with the diagram is attached below Could the answer be verified...
19. ### Gauss' law for uniformly charged space

the problem: Say we have the entire space uniformly charged. Then, the E field experienced by any point is zero, from symmetry.* But, it means that for any Gaussian surface, the flux though it is zero even though the charge enclosed is clearly not. Gauss' law seems to disagree with symmetry, but...
20. ### Modification in Coulomb's Law and its implications

If the coulomb's law instead of following an inverse square relationship, follows an inverse cube relationship, How would it affect an isolated charged conducting sphere? How would it's field vary within the volume and how would the volumetric charge density be affected? Please give in some...
21. ### Finding Total Charge from E-field

1. Homework Statement A static charge distribution has a radial electric field of magnitude $E = \alpha \frac{e^{-\lambda r}}{r}$ where λ and α are positive constants. Calculate the total charge of the distribution. 2. Homework Equations Gauss's law ##Q/\epsilon_0 = \int \vec{E} \cdot...
22. ### Gauss' Law: Charged Rod & Sphere (Electric Flux)

1. Homework Statement A charged, straight line/rod of infinite length has a Discrete uniform distribution of charge, has a linear density of λ and is at a distance d from a sphere with a radius of R. Find the entirety of the Electrical Flux that is caused by this charged rod, which passes...
23. ### Elec. flux through the top side of a cube with q at a corner

1. Homework Statement Find the electrix flux through the top side of a cube. The cube's corner is on the origin, and is 'a' units on length. The charge 'q' is located at the origin, with the corner of the cube. 2. Homework Equations Gauss's law and symmetry 3. The Attempt at a Solution I...
24. ### I Gauss' Law for electromagnetic radiation?

For the proof I've read that verifies transverse electromagnetic waves are consistent with Gauss' Law, there seems to be the suggestion that the magnetic and electric field at a given small length c(dt), along which the waves travel, propagate infinitely backwards and forwards in their...
25. ### Electric potential related to electric field question

1. Homework Statement (i) Consider a non-conducting sphere of radius R with non-homogeneous charge density ρ = ρ(r) = r, where r is the radial co-ordinate. (a) Find the electric field inside and outside of the sphere (b) Find and plot the electric potential inside and outside of the...
26. ### Electric potential of charged concentric spheres

1. Homework Statement Two conducting concentric spheres of negligible thickness. The radii of the spheres are R_1 and R_2, respectively, with R_2>R_1. A charge q_2 is placed on the external sphere. A charge q_1 is placed on the internal sphere. Assume that the electric potential is zero...
27. ### Capacitance capacitor parallel plate with dielectric (Gauss)

1. Homework Statement I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle. https://ibb.co/b0W4BQ 2. Homework Equations ∫D⋅ds=Q D=E+γP C=Q/V 3. The Attempt at a Solution Suppose the top plate has a...
28. ### Gauss' Law - electric field

1. Homework Statement An infinite metal plate has a surface density of charge σL=-6μC/m² , Left side and a surface density Of load σR=+4μC/m² , in the right side. A Gaussian surface In the form of a circular cylinder, with area A 12 cm², is Located with the left side inside the plaque and a...
29. ### Capacitor with uniform space charge between them

1. Homework Statement 2 large plates are seperated by a distance d and a space charge of uniform charge density p is placed between them and a potential difference V is applied accross the plates. Find the electric field stength at a distance x fromt the positive plate The answer is -V/d...
30. ### Electric field of a washer (hollow disk)

1. Homework Statement A washer made of nonconducting material lies in the x − y plane, with the center at the coordinate origin. The washer has an inner radius a and an outer radius b (so it looks like a disk of radius b with a concentric circular cut-out of radius a). The surface of the washer...