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 have charged particles having Brownian motion, would this motion be associated with (or produce) heat or electricity? Would it produce electromagnetic radiation (and if it would produce it, what type of radiation in the electromagnetic spectrum)? Could there be Brownian motion of charged...
If there are two charges positive and negative and their electric field point in the same direction then the total electric field would be their sum of magnitudes. Why don't we consider the sign of the charges? For example, a parallel plate capacitor is inside the region where both the positive...
Suppose you have an infinite plane of charge. If the surface charge density is uniform, would the tangential electric force always be zero, even if it is not a conductor nor static? My thought process for this is that if you look at each point charge and draw the electric field lines, then at...
I am confused about this, do the black arrows represent the direction of magnetic force?
The torque ##\tau = -IABsin\theta##, where I = current A is area of loop and B is magnetic field strength and I am a little confused how ##\theta## here is 45 degrees when the angle between the normal for...
I know how to solve the question but I am a bit confused about why there is a current of 3 A and a voltage of 110 V requirement for the refrigerator but the power plant only supplies 110 V.
How can there be a voltage drop on the refrigerator load of 110 V, when there is also a voltage drop on...
Electric field is 0 in the center of a spherical conductor. At a point P (black dot), I do not understand how the electric field cancels and becomes 0. Electric field is in blue.
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...
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...
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 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...
(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
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...
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: $$E =-...
Hello there, I have derived the expressions for electric field and potential to be the ones above, then for continuity at ##x = 0## I set the electric fields and potentials to be equal to yield the expressions:
$$Sx_p^2 = Kx_n^2$$
$$V_{bi} = V_n - V_p = \frac {q}{3\epsilon} \left( Sx_p^3 +...
The force on charge ##q_2## will depend on the electric field in medium with dielectric ##K_2##.
Electric field in this second dielectric due to ##q_1## is ##E = \dfrac {kq_1} {K_2r^2}## where r would be the distance from ##q_1##.
So, the electric field at the point where charge ##q_2## is...
I am wondering if the phase diagram of Carbon has been explored at very large electric fields.
Can one make any theoretical guesses ?
In specific I am interested in Pressure Vs Electric field and Electric field vs Temperature at fixed temperature and pressure respectively.
I pretend to use the ecuation twice, once for the interior and another for the vaccum, so if I use the cilindrical coordinates for \nabla_t^2 it results in two Bessel equations, one for the interior and another fot the vaccum.
In the vaccum, the fields should experiment a exponential decay, in...
A wavefront is defined as a surface in space where the argument of the cosine has a constant value. So I set the argument of the cosine to an arbitrary constant s.
## k(\hat{u} \cdot r - c t) + \phi = s ##
The positional information is is in r, so I rearrange the equation to be
## \hat{u}...
I am thinking about how an electric field has energy associated with it. If a single electron exists alone in a remote vaccuum, I believe it has it's own electric field surrounding it, and that this field has an energy content associated with it. My question is; does this electric field store...
I came across the following explanation from the famous book of Sears and Zemansky which I am unable to understand. I can get the initial part where a positive charge goes to the top plate of C1 since the point a is at a +ve potential causing free electrons to transfer from top plate of C1 to...
In my book, the potential gradient for a charge placed anywhere in space is defined as: E = -V/r
HOWEVER, for parallel plate (capacitors) the potential gradient is defined as E = V/d (V being the potential difference). How come there's no negative sign for the potential gradient of the parallel...
Dear friends,
First of all I have one question! As per Figure 1, how to implement electrical connection in real life which are seen inside Red Box? and what is the meaning of grounding the other terminal?
Figure 1
And the second thing is that, I want to create and electric field on copper...
I am trying to calculate the energy within an electric field that is generated between two plates by a pulse but am unsure of what voltage value to use. The pulse is a sinc wave.
I am assuming I can still use the equation ## E= \frac{1}{2}CV^2 ##. I know the ##V_{rms}## and ##V_{max}## which...
Hello everyone!
I've tried everything but the equation (3) in "Deflection of electrons in electrostatic field" is impossible. Can someone at least hint me to a a way the composed it ?
I think:
Due to charge q, there will be a field in region 1, very much dependent on position of q. The inner surface charge density of irregular conductor is also dependent on the position( so that it could cancel the field of charge and E=0 inside body of irregular conductor). The outer...
Hello everybody
To calculate the flux for the electric field I need the gauss law. There are two formula one with the integration over some area and the other is Q/e0. When do I have to use which one?
figure 1: →
I don't understand how to approach this problem. Basically it asks for the distance r.I think I should use Gauss's law, but I've been thinking about the shape of the gaussian surface and I'm not sure about how it should look or where I should place it. Any help would be...
For the first part, since
$$ E(r) \propto \frac{1}{r} \hat{r}$$
by the principle of superposition the maximal electric field should be halfway in between the two wires.
Then I'm not sure how to go about the second part of the question. I understand that the total potential due to the two wires...
F = qE
ma = (2*10^-6) * (λ / (2pi*r*ε0) )
ma = (2*10^-6) * (4*10^-6 / (2pi*4*ε0) ) => I am 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...
Attached is the subsection of the book I am referring to. The previous section states that the electric field magnitude at any point set up by a charged nonconducting infinite sheet (with uniform charge distribution) is ##E = \frac{\sigma}{2\epsilon_0}##.
Then we move onto the attached...
Here I am going to include the proof provided by my book. It is quite a splendid explanation, though there are a few key points I have yet to fully understand. If the electric force by the electric field on the charge at the surface of the conductor is conservative (which it is), then why is...
Let's say I place a positive point charge inside a hollow conducting sphere. If we take a Gaussian surface through the material of the conductor, we know the field inside the material of the conductor is 0, which implies that there is a -ve charge on the inner wall to make the net enclosed...
So for the Gaussian theorem we know that $$ \frac{Q}{e} = \vec E \cdot \vec S $$ Q's value is known so we don't need to express it as $$Q=(4/3)\pi*(R_2 ^3-R_1 ^3)*d$$ where d is the density of the charge in the volume. I've expressed the surface $$S=4\pi*x^2$$ where x is the distance of a point...
The charges are q1,q2 & q. P,Q,O1,O2 refer to positions only. This is a conducting sphere with cavities containing charges.
I'm interested in knowing how the charge should be distributed in the sphere. I know the charges induced on the charges of the sphere should be equal and opposite to the...