F = qE
ma = (2*10^-6) * (λ / (2pi*r*ε0) )
ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => Im not certain what to put for r ( But I sub in 4 because dist is 4)
a = ( (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) )/ 0.1
a = 0.35950
v^2 = U^2 + 2 a s
v = 0
u^2 = -2 a s => Can't sqrt negative so i...
I think the right solution is c). I'll pass on my reasoning to you:
R=6\, \textrm{cm}=0'06\, \textrm{m}
\sigma =\dfrac{10}{\pi} \, \textrm{nC/m}^2=\dfrac{1\cdot 10^{-8}}{\pi}\, \textrm{C/m}^2
P=0'03\, \textrm{m}
P'=10\, \textrm{cm}=0,1\, \textrm{m}
Point P:
\left.
\phi =\oint E\cdot...
When I try to do Gauss, the permeability is not always that of the free space, but it varies: up to a certain radius it is that of the void and then it is the relative one. How can I relate them? I'm trying to calculate the capacity of a spherical capacitor.
The scheme looks like this: inside I...
Homework statement:
Find the electric field a distance z from the center of a spherical shell of radius R that carries a uniform charge density σ.
Relevant Equations: Gauss' Law
$$\vec{E}=k\int\frac{\sigma}{r^2}\hat{r}da$$
My Attempt:
By using the spherical symmetry, it is fairly obvious...
The load system formed by the point load and the load distribution generates two regions in space corresponding to r<1m and r>1m, i.e. inside and outside the sphere. Given the symmetry of the distribution, by means of the Gaussian theorem we can find the modulus of the field at a distance r from...
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...
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...
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...
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...
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?
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
The...
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...
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
Homework Equations
The Attempt at a Solution
I...
Homework Statement
Compute the flux of a vector field ##\vec{v}## through the unit sphere, where
$$ \vec{v} = 3xy i + x z^2 j + y^3 k $$
Homework Equations
Gauss Law:
$$ \int (\nabla \cdot \vec{B}) dV = \int \vec{B} \cdot d\vec{a}$$
The Attempt at a Solution
Ok so after applying Gauss Law...
Homework Statement
Griffiths' Introduction to Electrodynamics problem 2.10,
Homework Equations
Gauss' Law, ##\int_{S} \textbf{E}\cdot \textbf{dS} = \frac{Q_{\text{enc}}}{\epsilon_0}##[/B]
The Attempt at a Solution
It seems reasonable that the flux through the shaded surface and the...
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...
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 b...
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...
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...
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...
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 of...
Homework Statement
Homework Equations
F=ma
F=Gm1m2/r2
Gauss' Law?
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.). From what I...
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 radius...
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...
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...
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...
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.
Homework Equations
Gauss's law ##Q/\epsilon_0 = \int \vec{E} \cdot d\vec{S}##...
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...
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.
Homework Equations
Gauss's law and symmetry
The Attempt at a Solution
I take 8 cubes...
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...