I know the energy is ##\frac{q²}{ 8 \pi \epsilon_{0}}( \frac{1}{a} - \frac{1}{b})##, but I can't get this result using the second equation.
What I did:
##W = \frac{1}{2} \int \rho V d \tau ##
##\rho = \frac{q}{ \frac{4}{3} \pi r³}, a < r < b ##
##V = \frac{q}{4 \pi \epsilon_{0} r}##
## W =...
Can we create at least any one of the following in laboratory? How?
1. A uniformly charged spherical shell of finite thickness
2. A uniformly charged sphere
3. A radially symmetrically charged spherical shell of finite thickness
4. A radially symmetrically charged sphere
I am required to find the direction of the electric field on the surface of a grounded conducting sphere in the proximity of a point charge ##+q##. The distance between the center of the sphere and the point charge is ##d## and using the method of images we find that the charge of the sphere is...
The final result will only differ in its sign, but this is crucial. Having a positively, radially oriented electric field ##\textbf{E}##, I understand that the sign of the integral should be positive (## - (- A) = A##), but it is not! How and why is this the case? A line integral where the...
What is true is that the field due to the point charge outside of the conductor will not be able to penetrate the shell i.e. there will be no field due to the external point charge anywhere within the conductor nor in the cavity: the field will be **killed off*& by the charges on the outer...
$$W = - \int _ { a } ^ { b } \vec { F } \cdot d \vec { r }$$
( The Force here is referring to the applied force, When moving a positive charge towards another positive charge(stationary) / field
In this formula why there is a negative sign in the formula? I am not asking the sign of the total...
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...
I'm interested in the following general question: Assume x,y,z is an axes system, and that the y-z plane is occupied by a conductive plate at a known potential V with respect to the earth. Now, a conductive material M of neutral global electrical charge is placed at some distance of the plate...
Homework Statement
Consider a conducting sphere with radius ##R## connected to a voltage source of ##V_0## volts. If the sphere is then covered by a dielectric spherical layer of radius ##9R## calculated the relative permitivitty ##\varepsilon_0## needed so that the field in the empty zone...
I have a non conducting sphere with a charge ρ=A/r per uni vollume A is constant. suppose there is a cavity in the centre and within a particle of charge q. i want to find the E inside the sphere in respect with r.
Homework Equations
The Attempt at a Solution
for radius equal of the cavity i...
Homework Statement
Find the field at A.
Homework Equations
##\oint E\cdot dA = Q_{enclosed}/\epsilon_0##
The Attempt at a Solution
My first intuition was to do a Gaussian cylinder from A to the middle of the bottom plate. My logic is that the field inside the bottom plate is 0, so I'd have...
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) State the boundary conditions for the electric field strength E and electric flux density D at a planar interface separating two media with dielectric constants ε1 and ε2.
b) A parallel plate capacitor with a plate separation d is filled with two layers of different...
Statement
Four point charges, Q, -Q, Q, -Q, are placed at the four ends of a horizontal square of side a as shown in the figure above. What are the neutral points?
The attempt at a solution
The square is not exactly aligned parallel in its plane, say XY.
So, the center is not a neutral...
Homework Statement
A semi-circular wire containing a total charge Q which is uniformly distribute over the wire in the x-y plane. the semi-circle has a radius a and the origin is the center of the circle.
Now I want to calculate the electric field at a point located on at distance h on the...
In the classical electromagnetic field theory, the field density of energy is given by:
$$u = (\epsilon/2)E^2 + (\mu/2)H^2$$
One of the differences between the classical electromagnetic theory and the real world is that in classical EM all charge and current density, (ρ(r), J(r)), is...
1. Homework Statement
A simple model atom is composed of a point-like nucleus with charge ##+Q## and an electron charge distribution
$$
\rho(\vec{r})=-\dfrac{\left|Q\right|}{\pi a^2 r}exp(-2r/a)
$$
where ##a## is a constant. Show that the ionization energy (the energy to remove the electron to...
Homework Statement
We have a spehere of radius ##r_1## and on of ##r_2## far away from each other. The first sphere has a charge ##Q##. What is the change in electro static energy when they are connected together?
Homework Equations
Potential of a charged sphere: ## V = \frac{Q}{4\pi\epsilon_0...
Homework Statement
We want to calculate the field of a uniformly polarized sphere of radius=R
Homework Equations
V(\vec{r}) = \frac{1}{4 \pi\epsilon_{0}} \oint_{S} \frac{\sigma_{b}}{r} da' + \int_{V} \frac{\rho_{b}}{r} d\tau'
The Attempt at a Solution
i)I know that
\sigma_{b} = P...
1. In above image an insulated metal plate has been placed inside earth (soil), and an voltage is applied between plate and earth groung what will be the capacitance here??
2. one plate is the metal and the other plate is entire earth, so it is a big assymetrical Capacitor or What?
all...
Homework Statement
[/B]
In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l,w and d, respectively.
A uniform magnetic field B is applied on the strip along the positive...
Homework Statement
[/B]
I have two spherical metallic shells with radius ##3a## and ##a##, the little one is placed inside the larger so that the center of the little one is at a distance of ##a## from the center of the larger. The outer one has a charge ##3Q## and the one inside has a charge...
hi, i still don't understand why infinite thin-walled cylindrical shell or conducting rod use lambda rather than sigma ?
lambda = C/m ,,, sigma = C/m^2
i mean when we look at conducting rod, the charges inside the conductor is zero, so the charges spread on the surface of conducting rod(have...
Homework Statement
A proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 3×10-15 m and calculate the potential energy of the subsystem of...
Hello,
It's a theoretical question. I take 2 electrostatic particules fixed in a circle. I turn the circle. Is there a magnetic field ? I suppose the angular velocity very high and I suppose the particules are fixed in the circle. The diameter of the circle is very small. I don't want the...
I'm looking at equipment that scans an image through a feeder....... evidently dust build up could be a problem.
Thinking of a piece of paper, that might attract dust, that could be run through it (I saw a vid of a piece of cleaning paper run through a system - I'm presuming it is 'dust...