All Questions
Tagged with electromagnetism definite-integrals
18
questions
1
vote
3
answers
152
views
$\int_0^R \frac{r^{l+1}}{\sqrt{R^2 - r^2}}\text dr$
I'm trying to solve problem 3.3 from Jackson's Classical Electrodynamics, but I'm encountering some troubles solving
$$
\int_0^R \frac{r^{l+1}}{\sqrt{R^2 - r^2}}\text dr,
\qquad l = 0,2,4,6,\ldots
$$
...
- 135
2
votes
0
answers
29
views
Does this family of curves appearing in the magnetic field of a coil have a name?
While attempting to express the magnetic field induced by a single coil of current (at any point in space, not just on the coil's axis), I tried visualising the set of the infinitesimal contributions $...
- 165
2
votes
1
answer
85
views
How to evaluate the integral $\int_{-r/2}^{r/2} \int_{-r/2}^{r/2} \frac{1}{x^2+y^2+r^2/4} dx dy$
I came across this integral while trying to evaluate the electrical force exerted by a charged plate in the form of a square with side length $r$. I tried the usual method of first keeping $y$ ...
- 409
0
votes
1
answer
55
views
I was trying to find field due uniformly charged sheet at a distance h from centre of the square sheet
I assumed the square(side a) sheet to be made up of wires.$$dE=Kdq/r^2$$
The field due to a wire is : Reference
$$\frac{K\lambda}{d}\left[\frac{x}{\sqrt{d^2+x^2}}\right]^{(a/2)}_{(-a/2)}=\frac{K\...
- 471
6
votes
1
answer
111
views
What is the value of $\frac{1}{2}\int_B\int_B\frac{\rho(x,y,z)\rho(x',y',z')}{4\pi\epsilon_0\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}}dxdydzdx'dy'dz'$?
I am reading a book about electromagnetism by Yousuke Nagaoka.
Suppose $R$ is a positive real number.
Suppose $Q$ is a positive real number.
Let $B:=\{(x,y,z)\in\mathbb{R}^3:\sqrt{x^2+y^2+z^2}\leq R\}...
- 8,740
4
votes
5
answers
216
views
How to calculate $\int_0^{2\pi}\frac{\cos(\phi)-R}{1-2R\cos(\phi)+R^2}\cos(n\phi)~d\phi$?
I wish to calculate
$$I(R)=\int_0^{2\pi}\frac{\cos(\phi)-R}{1-2R\cos(\phi)+R^2}~\cos(n\phi)~d\phi,$$
where $n\in\mathbb{N}$, $R\in[0,1)$.
Based on trial and error from plugging numbers into Wolfram ...
- 1,027
2
votes
1
answer
187
views
Calculating the average of the square of the magnitude of an electric field
Let the sinusoidal electric field polarised in the $\hat{x}$ direction be $\overline{\mathcal{E}}(x, y, z, t) = \hat{x}A(x, y, z)\cos(\omega t + \phi)$, where $A$ is the amplitude, $\omega$ is the ...
- 4,322
2
votes
0
answers
66
views
Flux of the horizontal Electric field through a hemisphere
Suppose I've a hemisphere and an electric field passing horizontally through this hemisphere. I need to find the flux of this field through this hemisphere.
I can easily consider the electric field to ...
1
vote
0
answers
35
views
Deriving force between continuous distributions of two volume charges without using infinitesimals
We know that force between two point charges is:
$$\vec{F}=k\ q\ q'\ \dfrac{\hat{r}}{r^2}\tag1$$
From here how shall we derive the equation for force between continuous distributions of two volume ...
- 1,141
5
votes
1
answer
162
views
Evaluate Integral $ I:=\int_0^{2\pi} \cos s \,\log (\sqrt{c^2 + a - 2 \cos s}-c) \, \mathrm d s $ for radially magnetized cylinder
When trying to evaluate the magnetic scalar potential $\Phi_m$ of a magnetized cylinder (Magnetization $M$ in $x$-direction, height $Z$, Radius $R$, touching the $xy$-plane from below), I was able to ...
- 81
0
votes
1
answer
123
views
Electric Field and Direction of Field
I want to measure the magnitude, and the direction of the electric field at point P induced by a rod that has a charge of $-22.0\mathrm{\mu C}$. The problem has been accurately dimensioned. The ...
- 2,653
0
votes
0
answers
49
views
What is wrong here?
What is wrong in turning this expression in spherical coordinates :
$$\int_{0}^{\pi}\int_{0}^{2\pi}\vec{r}\, \cos \Theta \, \sin \Theta \, \mathrm{d} \Theta \, \mathrm{d} \phi $$
to this :
$$\...
0
votes
2
answers
239
views
Evaluate $\int_0^{2\pi}\ln(1+a^2-2a\cos(x))dx\text{ ,with }a>0$ [duplicate]
$$\int_0^{2\pi}\ln(1+a^2-2a\cos(x))dx,\;\;\;\;\text{with }a>0$$
How to evaluate Integral of $\ln(1+a^2-2a\cos x) dx$? where $x$ from $0$ to $2\pi$ and $a>0$, $\ln$ is the natural logarithm.
- 422
0
votes
1
answer
105
views
Why am I not getting the right answer for this integral?
I'm trying to solve the integral below. I'm not getting the right answer no matter what. Can you tell me why my method is wrong? I'm applying the rule for integrating $x^n$ (i.e. $\smash{\frac{x^{n+1}}...
- 93
0
votes
0
answers
38
views
What is the solution to the following integral? Dirac Delta function must be invoked at some point.
Evaluate the following integral,where is the usefulness of the delta function in the evaluation?
$$\int_{-\infty}^{\infty} f(r)\nabla\frac{\vec{r}-i}{(r-i)^3} dr$$
