Understanding Electromagnetics with Limited Time: A First Assignment Dilemma

[drobertwilcox]

I'm working on my first assignment in an EM class and I have a couple questions (this might be a long post). Understand I'm a part time student and I live an hour away from the university and work 40+ hours a week... time is limited. I have a 5 problem assignment and a million questions.

Homework Statement

1. For a given charge system, the flux density D= r^2sin(theta)ahat_r+sin(theta)cos(phi)ahat_phi C/m^2. Determine

a)the Charge density at point (1m,45 deg, 90 deg)
b)Find the force on a point charge of 1nC located @ (1m,1m,2m)

Homework Equations

a) Plug the point into the flux density?
b) convert spherical to cartesian coordinates find R(trig) and coulombs law for charges in free space 9x10^9(Q_1Q_2/R^2)

The Attempt at a Solution

a)so from my understanding a charge density requires a surface area, I am supplied with a point so I thought I'd just put the point in the equation and evaluate from 0 to 1 0 to 45 and 0 to 90... everything cancels but root2/2 which I believe is my answer but I have a point not a surface area.

b)I find R to be root6 using the given charge and the found charge from the previous part put into coulombs law yields 3root2/4 N



The next question is a potential question and I'm lost

The potential field with Epsilon_r = 10 is V=12x^2y find E, P, and D

I don't know where to begin,


3) a square conductive loop 10cm/side is centered at origin carries 10mA current clockwise viewed from the +z direction find the magnetic field intensity at point (0,0,10)

I have sketched it out and found the distance from the point to the corner to be root110 and the shortest point to the line to be 5root2, all the evaluations I can find that come close to this problem all use circles around the point not squares... I'm lost

it sound's like and Ampere's Law problem
intH dot dl = I enclosed


4) Given the magnetice field H=3y^2ahat_y A/m find the current passing through a square in the xy-plane that has one corner at origin and the opposite corner at (2,2,0)

sounds like the opposite of the last problem still stuck


5) in a given region of space, the magnetic vector potential is given by A=5cos(pi y)xhat+(2+sinpix)zhat (Wb/m) determine B and flux passing through a square loop with 0.25 m long centered at the origin of the xy plane and its edges are parallel to the x and y axis.

?

I haven't dug into the lecture notes and book for this one yet this is due next monday... like I said it's my first assignment and we haven't worked any practice problems in class. I want to understand the correlations between current and magnetic field... that would help with 3&4. Any direction on this assignment would be greatly appreciated.

Thank you

David

 

[drobertwilcox]

2) -gradient V = E
dv/dx 12x^2y + dv/dy 12x^2y + 0 = -24xy-12x^2 = E
D=epsilon E ; epsilon_o E+P; P=epsilon_o chi_e E

 

[CarlB]

Okay, I'm lousy at E&M but I'll take a whack.

For the force on a particle, that's easy, you need to find a law [i.e. get the units right] that is going to look something like
F= qE + v\times B
Now I'm writing "E" and "B" cause I'm interested in elementary particles and we don't have "D"s or "H"s there.

The relationship between charge density \rho and E (or D, I guess) is going to be an equation that will look something like:
D = \nabla \rho
plus something I've forgotten that may have to do with a changing magnetic field... But this early in the course you probably are doing problems in statics, i.e. electrostatics.

So to solve that problem you will have to do an integral. Which, hilariously, means that the problem is ill posed. You can always add a constant charge density to \rho and end up with the same electric field. However, in requiring that \rho(x) \to 0 as x \to \infty, you will probably be able to find a unique solution.

 

[BNoelCMU]

To solve the first problem, you need to use Gauss's Law, which is ACTUALLY div D = rho. So, take the divergence of D, in spherical coordinates (it should be somewhere in your EM book, or you can find it in a multivariable calculus book). You will end up with an expression that is a function of R, theta, and phi. From there, you can just plug in for that particular point and you have the charge density.

For the second part, you can just use the relationship F = qE. Figure out how E and D are related, and remember that you are working with vectors and vector fields.

Next question: given a potential field, you can use the fact that E = -del V to get E. E, P and D are all related so look through your notes to get those relationships.

 

[drobertwilcox]

it's done thank you for the pointers

 

[CarlB]

To solve the first problem, you need to use Gauss's Law, which is ACTUALLY div D = rho.

Yeah! That will be a lot easier. And it might get the right answer, LOL.