I used the potential at the surface of the sphere for my reference point for computing the potential at a point r < R in the sphere. The potential at the surface of the sphere is ## V(R) = k \frac {Q} {R} ##.
To find the potential inside the sphere, I used the Electric field inside of an...
The problem is for a solid sphere uniformly charged with Q and radii R.
First I calculated taked ##V(\infty)=0##, giving me for :
$$
\begin{align*}
V(r)=&\frac{3Q}{8\pi\varepsilon_0 R}-\frac{Q}{8\pi\varepsilon_0 R^3}r^2\qquad\text{if $r<R$}\\
V(r)=&\frac{Q}{4\pi\varepsilon_0 r}\quad\text{if...
Let us connect a battery of potential difference V to a wire. There is no resistance. Nothing!
Now the battery creates some potential difference and the charges in the conducting wire move due to the Electric field created in the conductor by the battery. So, as the charge moves, its potential...
Hi,
I think this problem is solved in exactly as a similar problem where the two spheres are very far apart and connected by a very long thin conducting wire. I'm trying to explain this in words, since LaTeX does not seem to work any more (for some reason LaTeX syntax is not replaced by maths in...
This is in python:
#ELECTRIC POTENTIAL
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import numpy as np
import matplotlib.pyplot as plt
dx = 0.1
dy = 0.1
xrange=np.arange(-1,1,dx)
yrange=np.arange(-1,1,dy)
X,Y = np.meshgrid(xrange, yrange)
max_dV = 10e-5
blockRadius = 3...
A rod with a circular center in the middle (which causes the rod to change direction by 90 °) has an evenly distributed linear charge density 𝜆 of electrons along the entire rod. Determine the electrical potential of the red dot in the figure below which is at the center of the circular round...
Summary:: if Plate A had a potential of 9V, This means as We approach a unit charge from +Infinity to A we have to do this precise amount of work
Now we remove plate A, And replace it with plate B that has a potential of -9V Again that means to go from +Infinity To B we actually gain energy, or...
Imagine a container of salt water at 0V (Relative to ground),Now you've put in it 2 electrodes,one at +500V (Electrode A), The other at +250V(Electrode b), Normally positive ions should go to the negative electrode , and Negative ions should go to the positive electrode , But in our example the...
V(ρ) = V_o*ln(ρ/0.0018)/ln(45/180)
(Attached picture is where the unit vector of r is really ρ.)
In cylindrical coordinates
∇V = ρ*dV/dρ + 0 + 0
∇V =derivative[V_o*ln(ρ/0.0018)/1.386]dρ
∇V = V_o*0.0018/(1.386*ρ)
E = V_o*0.0012987/ρ
Work = 0.5∫∫∫εE•E dv
Bounds: 0.0018 to 0.00045 m
D = εE =...
If we set the potential at infinity to be zero, we find that the potential of a grounded conductor is V=0. The conductor being grounded has no net charge and produces no external field, so I understand why in that situation we would say the potential of the conductor is zero.
However, in...
So I figured out the potential is: dV = (1/(4*Pi*Epsilon_0))*[λ dl/sqrt(z^2+a^2)]
.
From that expression: We can figure out that since its half a ring we have to integrate from 0 to pi*a, so we would get:
V = (1/(4*Pi*Epsilon_0))*[λ {pi*a]/sqrt(z^2+a^2)]
In that expression: a = sqrt(x^2+y^2)...
Summary: Potential at origin of an infinite set of point charges with charge (4^n)q and distance (3^n)a along x axis where n starts at 1.
From V=q/r, we find Vtotal=sum from 1 to infinity of (4/3)^n(q/a), which diverges. There cannot be infinite potential because there is a finite electric...
Hi,
having not a deep knowledge of electrochemistry I've some doubts about processes involved in a galvanic cell. Take for instance a Zn/Cu Daniell cell for which E0cell is 1,10V. That means emf for it is 1,10V.
Starting to read from how battery works I had a first understanding of how...
I) For the first part I used:
##V = - \int E ds = \int_a^c \frac{1}{4\pi\epsilon_0} Q /r^2 dr+ \int_c^{c+d} \frac{1}{k} \frac{1}{4\pi\epsilon_0} Q /r^2 dr + \int_{c+d}^b \frac{1}{4\pi\epsilon_0} Q /r^2 dr ##
And by using ##C = Q/V## We get an answer which is somehow large for writing here...
Hi,
I've a question about electricity in the following scenario: consider an accumulator (e.g. a 9V battery) and an analog/digital voltmeter having a probe connected to the accumulator + clamp and the other to the ground (for instance connecting it to a metal rod stuck in the ground).
Do you...
Homework Statement
The solution to this problem is B, and I was able to get the answer by calculating the total potential at ##r = 2a##, however, what I don't seem to understand is why must the voltage be calculated at ##r=2a## but not ##r=3a##.
Homework Equations
##V(r) = - \int_a^b E(r)...
When I first learned about these subjects, I did what was intuitive to me and treated particles as if they carried potential energy. I would do this similarly for rigid bodies where I would also treat them as a particles with their body's mass at the center of mass. This wasn't helped by...
1. The problem statement
Two charges of 3μC and -2μC are placed 2cm apart. At what point along their connecting line is electric potential zero?
Homework Equations
Electric potential superposition Φ=Φ1-Φ2 since q2 is negative
Φ=kq/r^2
The Attempt at a Solution
Let’s say the charges are on the...
Homework Statement
We have an uncharged, conducting wire with radius a. We surround it by a linear dielectric material, εr, which goes out to radius b. We place this in an external electric field, Eo.
Homework Equations
We have electric potential inside (a < s < b)
Vinbetween=Acosφ +...
Homework Statement
We have the cross section of a metal pipe that has been split into four sections. Three of the sections have a constant electric potential, Vo. The fourth section is grounded so electric potential is zero. We are looking for electric potential inside and outside of the pipe...
So in my textbook (Introduction to Electrodynamics by Griffiths) it said that inside a conductor, the electric field E would have to zero, since if it wasn't the free charges would move accordingly and create a electric field that cancels the original field. But in a question that soon followed...
Homework Statement
I'm given that there is a positive charge of 1 nC at x=0.25 m and a negative charge of -1 nC at x=-0.25 m. I've calculated the potential created at different points along the x-axis by the positive charge and the negative charge using the formula, $$V=\frac{kq}{|r|},$$ where...
Homework Statement
A plane z=0 is charged with density, changing periodically according to the law:
σ = σ° sin(αx) sin (βy)
where, σ°, α and β are constants.
We have to find the potential of this system of charges.
Homework Equations
The Attempt at a Solution
[/B]
I...
Homework Statement
A solid insulating sphere of radius a = 3.6 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -215 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 11 cm, and...
At the interface between:
1) conductor/conductor
2) conductor/semiconductor (or dielectric)
3) semiconductor/semiconductor (or dielectric/dielectric)
What quantity should be continuous?
Is it the electrochemical potential, only the chemical potential or is it the electric potential?
Since they...
Please refer to the image attached. So, my doubt is:
While calculating dW in the derivation, we know this work is being done by external force, because only then the unit positive charge can be made to move towards the charge +Q. So dW should be equal to Fext.dx but here in the book it is shown...
Hi I have a question about electric potential! Since the negative sign isn't used in U=qV, and a-b is used for subscripts, then that takes care of the negative. But what about using U=-qV? An online lecturer uses U=-qV, while my textbook uses U=qV and then uses -qV to explain the force used to...
Homework Statement
The electric field inside a parallel plate capacitor is measured to be E= -3500 N/C i. The electric potential at point XA = 3.00 m is measured to be 1500V. What is the electric potential at point XB = 0 m?
Homework Equations
V=E⋅s
The Attempt at a Solution
I think I need to...
So here is how my book defined electric potential. If you take a charge, it will have a corresponding electric field associated with it. If you put another charge in that electric field, an electrostatic force will act on it and give it kinetic energy. This kinetic energy can't come from thin...
So I've been learning how batteries work. What I learned is that a battery consists of 2 pieces of metal both with different electronegativities. These metals react with an electrolyte.
One metal (called the anode) is oxidized and has its electrons removed, leaving behind a positive ion which...