What is Electric field: Definition and 1000 Discussions
An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges, or from time-varying magnetic fields. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.
Electric fields are important in many areas of physics, and are exploited practically in electrical technology. In atomic physics and chemistry, for instance, the electric field is the attractive force holding the atomic nucleus and electrons together in atoms. It is also the force responsible for chemical bonding between atoms that result in molecules.
Other applications of electric fields include motion detection via electric field proximity sensing and an increasing number of diagnostic and therapeutic medical uses.
The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The derived SI units for the electric field are volts per meter (V/m), exactly equivalent to newtons per coulomb (N/C).
If we put a positive charge outside of a conductor, there is an induced charge, but if we put a positive and negative charge inside a conductor, there is no induced charge?
1) Why is the electric field 0 at the bottom of Gaussian surface? Isn't the electric field on both sides of the surface, pointing down and outwards like a plane of charge? see image.
2) Why does a charge distribution with cylindrical symmetry have to be infinitely long?
3) My book says a...
The solution says that the tension in the string in the negative x direction is balanced by the force of the plate on the ball (red). Why is the repulsive force of the ball on the plate (in blue) not included in this calculation?
Does the electric field vector takes into account the field's radial direction? Usually when we calculate the electric field, we use ##\vec E = \frac{kq}{r^2}\vec j##, which is a straight line vector of a positive charge q's electric field. This electric field points from a positive charge q to...
What I don't understand is how come the electric field of the negative plane isn't pointing towards the positive plane (in blue) and cancelling out the electric field of the positive plane (in red). See image
Hello everybody,
I was visualizing the electric field radiation pattern of an antenna in a 3D EM simulation software (CST), and to see it with my eyes made me realize something I probably heard during my studies but forgot. What is the phenomenon behind what you can see below, which is the...
3 cm is inside the cylinder. We can use a gaussian cylinder to enclose the inside of the cylinder up to 3 cm. Because the outer cylinder is infinite there is no flux out of the end caps with the inner cylinder. There is also no charge enclosed in the cylinder. So the electric field 3cm away from...
If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...
At point ##P(0,0'03,0'04)## the field caused by the sphere is added to the field caused by the plane.
First, ##E_\sigma##
$$E_\sigma=\dfrac{\sigma}{2\varepsilon_0}=\dfrac{0,2\cdot 10^{-6}}{2\varepsilon_0}=11299,44\, \textrm{V}/\textrm{m}$$
Then, ##E_0##: Because ##r<R##...
I have the calculation of the electric field created by a ring of radius ##R## uniformly charged with a linear density of charge ##\lambda## at any point on the axis perpendicular to its surface (##z## axis), but I have some doubts about it. I'll leave you the calculation done first:
In ##x##...
Hello!
I am trying to solve this exercise of the electric field, but it comes out changed sign and I don't know why.
Statement: On a straight line of length ##L=60\, \textrm{cm}## a charge ##Q=3,0\, \mu \textrm{C}## is uniformly distributed. Calculate the force this linear distribution makes...
Draw a Gaussian pill box that starts from 0 (half way between the slab) and extends towards 2 cm.$$A \times \int_{0}^{0.02} \rho dz$$
I'm not sure if I should multiply the integral by A (area) or V (volume)
And if area would I multiply by 0.02^2?
I'm confused here. Thanks for your help.
Hey, I have a really short question about electrostatics.
The boundary conditions are :
\mathbf{E}^{\perp }_{above} - \mathbf{E}^{\perp}_{below} = -\frac{\sigma}{\varepsilon_{0}}\mathbf{\hat{n}} ,
\mathbf{E}^{\parallel }_{above} = \mathbf{E}^{\parallel}_{below}.
My question is what is...
define charge at an infinitesimal length of arc
$$dQ = \lambda R d \theta$$We only care about the x component of the electric field because the y components cancel due to symmetry
$$dE_x = \frac{k_e dQ}{R^2} cos \theta$$
Integrate to add up the infinitesimal parts. A quarter circle means 90...
We know the net force on the charged particle in the uniform electric field pointing up is mg - qE.
To get acceleration, divide the net force by mass to get g - qE/m
Plug into kinematic equation and get velocity by itself and substitute$$\sqrt{h(2g - \frac{q \sigma}{\epsilon_o m})}$$
λ1 = 3 microC/m λ2= -4 microC/m
__________ . __________
l----L1---l-a1-l-a2-l-----L2---l
(Not to scale)
L1 = length of rod 1 (1m)
a1 = length of end of rod 1 to point (0.7m)
L2 = length of rod 2 (1m)
a2 = length of end of rod 2 to point (0.3m)
k = e field constant...
Hi ...
How can I find the electric field due to a thin circular ring of radius a and charge q for points outside the plane of the ring?
The distance from the center of the ring to the point of the electric field is large compared to the radius of the ring.
I have answered it but I don't know if...
A nuclear reactor is built to fuse two hydrogen atoms that are already ionized to protons. However, the electric field of the protons are becoming a significant obstacle. If the reaction was to be defined as H2--> 2H++2e-, if the mass of a proton is mp, the radius of a proton r the charge of an...
I'm having an exam soon so i want to make sure. Is the electric field here zero?? cause if i draw gauss surface covering both of them they should cancel out or am i wrong.
I know that inside region 1, the D-field is zero as it is a conducting sphere, the E-field must be zero. It makes sense that in region 2 (inside the dielectric) there is a D-field.
My question is, is there a D-field outside the dielectric material (r>R)? Obviously there will be an E-field, but...
If a electrically charged mass travels thru a magnetic(m) field, it will accelerate at right angles to its velocity and the m-field. Under some conditions like this the charged mass will travel in a circular loop due to this magnetic force acceleration. This info is all over the internet. e.g...
I believe I have all parameters set up correctly to evaluate part A of this problem but I am unsure of the bounds.
I can't integrate from 0 to R because that part of this sheet has a hole there. I need to integrate from R to the other end of the sheet.
Im not sure how I would figure out the...
I wanted to post my work so far to see if I am on the right path toward the correct answer so far.
I have attached a ss of the actual problem and my work in the attachments
Im having trouble understanding the wording to this problem. When it says "from r=0 to r=infinity". My Qenc would zero out. I guess it makes sense that from infinitely far away you wouldn't "feel' the electric field but considering this question leads to 4 other questions I don't think I am...
I've calculated the intensity for every point charge which are
EA = 6.741 x 10¹³ NC¯¹
EB = 4.494 x 10¹¹ NC¯¹
EC = 6.741 x 10¹³ NC¯¹
and I am pretty sure about this far but I am struggling to calculate the X-axis intensity and Y-axis intensity to find the entire approximate intensity with the...
I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help.
The torque on a dipole can be defined as
τ=PEsinθ
The work done on a dipole to move it from an angle ##\theta_0##...
Hi,
We know that a varying magnetic field creates and induced electric field, and a varying electric field creates an induced magnetic field.
If there is a varying electric field (let's say sinusoidal), then this electric field creates an induced magnetic field. And if this produced magnetic...
By measuring angle \theta from the positive ##x## axis counterclockwise as usual, I get ##d\vec{E}=k( (\lambda_2-\lambda_1)\cos(\theta)d\theta, (\lambda_2-\lambda_1)\sin(\theta)d\theta )## and by integrating from ##\theta=0## to ##\theta=\frac{\pi}{2}## I get...
Hello everyone,
I was asking myself about electric field strength estimation at a distance d from - in my case - a half wave dipole antenna.
There are pretty much a lot of information about this on internet or in books but still, there are a few things that are confusing to me that I would...
According to theory I should be able to get the Electric Field (E) from its pOtential (V) by doing the grad (V) so
E = -grad(V), however, V is contant V = k*lambda* pi which results having E =0, but this is not right. What I am missing??
see figure below
The answer should be Ex = 2*k*lambda / r...
From the second equation I get that,
##\vec D =\frac{q}{4\pi \vec r^2}\hat r##
From first equation I get that
##\vec E = \frac{q}{4\pi \vec r^2 \epsilon}=\frac{q}{4\pi \vec r^2 K \epsilon_0}##
But I saw that the answer is ##\vec E=\frac{\vec E_0}{K}##
While writing the comment my mind said...
The dielectric strength of air (ie the maximum electric field that the material can withstand under ideal conditions without undergoing electrical breakdown and becoming electrically conductive) is 3 000 kV ( https://en.wikipedia.org/wiki/Dielectric_strength#Break_down_field_strength ).
In...
So I have been given a uniform electric field ##\vec{E}=20 V/m## in the direction as show in the image. I have been told to calculate the potential difference ##VC - VA##. According to the teacher (on YouTube) the potential difference ##VC - VA = -10\sqrt{2}V##. But I say it's ##-20 V## as...
(a) Knowing ##E##, we can use equation (2) to determine ##V##. However, since ##\vec E## represents the distribution of electric field in space i.e. a function of (x,y,z). For example, ##\vec E = x \hat i + y \hat j + z \hat k##. Here we do not know this function so how can we know ##V## at a...
Electric Flux = E*A = 5*6(0.05)^2.
when i look up at other sources they use Electric flux = q/ (8.854*10^-12 [this is e]) equation
but I am confused on why the E*A equation don't work. The answer is 0.02Nm^2/C
As shown in figure below, the electric field E will be normal to the cylinder's cross sectional A
even for distant points since the charge is distributed evenly all over the charged surface and also the surface is very large resulting in a symmetry. So the derived formula should also apply to...
When we connect tungsten filament light bulb to the battery, filament becomes hot due to electrons losing kinetic energy in the electric field inside of conductor. Heat is eventually converted to electromagnetic radiation making light bulb shine. Light energy comes from flow of electrons and...
What am I missing?
I also don't get the title of the section: "Charge distributions with enough symmetry for Gauss's Law".
I thought Gauss's Law was valid for any closed surface enclosing a charge. I don't understand what "enough symmetry" means in the title above. I get that with symmetry...
Using Gauss's Law
By using a symmetry argument, we expect the magnitude of the electric field to be constant on planes parallel to the non-conducting plane.
We need to choose a Gaussian surface. A straightforward one is a cylinder, ie a "Gaussian pillbox".
The charge enclosed is...
I am interested in particular in the second integral, in the ##\hat{r}## direction.
Here is my depiction of the problem:
As far as I can tell, due to the symmetry of the problem, this integral should be zero.
$$\int_0^R \frac{r^2}{(x^2+r^2)^{3/2}}dr\hat{r}$$
I don't believe I need to...
The strategy will be to figure out what ##dq##, ##\hat{r}_{dq,p}##, and ##r_{dq,p}## are, plug them into the expression for ##d\vec{E}_{p_r}##, then integrate over ##d\vec{E}_{p_r}## to obtain ##\vec{E}_{p_r}##, the electric field at ##P## due to the arc on the right.
Then I will repeat the...
Hi all,
I have a doubt when calculating the electric field of a uniformly polarized cylinder P along its longest axis. The cylinder has length L and radius a.
Using Gauss's law:
$$\int D\cdot ds = \rho_{f} =0 \, \, (eq .1)$$
The electric field inside of cylinder would be: $$E =-...
The net Electric field(inside the dielectric):
$$E_{net} = \frac{1}{4\pi \varepsilon_0 \varepsilon_r} \frac{q}{r^2}$$
$$\vec E_{net} = \vec E_{applied} - \vec p$$
where p is the polarization vector.
let charge ##q_{-}## be present on the inner surface of dielectric and ##q_{+}## on the outer...