# electromagnatism

1. ### Capacitor Energy With Different Dielectrics

Homework Statement Two parallel plates are connected to a battery which maintains a constant potential difference of 12.0 V. The distance between the plates can be varied and there are three plates of different dielectric materials available: rubber (0.40 mm, κ = 6.7), glass (4 mm, κ = 7) and...
2. ### Electric field between inner and outer cylinder

Homework Statement A capacitor is constructed of two long concentric metal cylinders, each having length of 1.0 meters. The inner cylinder has a radius R1 = 1.0 cm, and the outer cylinder has a radius R2 = 1.25 cm. The hollow space between the two cylinders is filled with nylon having a...
3. ### Proof that disk of charge = point charge when very far?

Homework Statement Take the expression 21.11 (pictured below, specifically the bottom one) for the electric field above the center of a uniformly charged disk with radius R and surface charge density σ, and show that when one is very far from the disk, the field decreases with the same square...
4. ### Refraction index

Homework Statement Within a certain material, an EM wave with = 1 mm is attenuated to 10% of its original intensity after propagating 10 cm. Determine the imaginary part of the index of refraction ni 2. Homework Equations 3. The Attempt at a Solution so...

I am confused with the fact of radiation pressure on Wiki and my homework solution. They are both arguing that the pressure produced by a ray of light to be reflected with incident angle θ and intensity I is: $$\frac{2I\cos^2(\theta)}{c}$$ My thinking We know that: $$Ft=\Delta p$$ We see the...
6. ### Modes orthogonality in a dielectric slab

A typical mode in a dielectric slab like this, with propagation along x, uniformity along z and refractive index variation along y, is represented by the following function: f (y) = \begin{cases} \displaystyle \frac{\cos (k_1 y)}{\cos (k_1 d)} && |y| \leq d \\ e^{-j k_2 (y - d)} && |y| \geq d...
7. ### Magnetic field of a long solenoid

Homework Statement A long solenoid has current I flowing through it, also denote N as the turns per unit length. Take its axis to be the z-axis, by symmetry the only component of the magnetic field inside is Bz. Find the magnetic field at the center of the solenoid (on the axis). Also, find the...
8. ### Potential inside a sphere with two regions

Homework Statement Suppose a charge is distributed in a lower half region of a sphere and the upper half has zero charge. What is the potential inside? Homework Equations Poisson Equation? The Attempt at a Solution My problem here is I don't know how to start, I think laplace equation can't...
9. ### Wave reflection and refraction, relations between angles

Hello! This post is strictly related to my previous one. Let's consider the same context and the same image. Regarding the oblique incidence of a wave upon an interface between two dielectric, all the texts and all the lectures write an equation like the following: e^{-j k_1 y \sin \theta_i} +...
10. ### Potential inside a grounded conducting sphere

Homework Statement Hi, I'm currently answering a problem in Jackson's electrodynamics. The question is: Given a point charge q inside a hollow. grounded, conducting sphere of inner radius a. Find the potential inside. This can be solved by placing an image charge outside the sphere, and...
11. ### B Magnetic permeability...

Who is credited for deriving the value of magnetic permeabilty in a classical vacuum? How would one go about sourcing information in relation to such a value?
12. ### Electrical Potential Energy of three quark system

Homework Statement A proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 3×10-15 m and calculate the potential energy of the subsystem of...
13. ### Determine charge at origin, based on charge density function

Homework Statement a) and b) are no problem. I need help to solve c) and d) Homework Equations c) Delta dirac function Gauss' law d) Gauss' law $\int_V {\rho \, d\tau} = Q_{enclosed}$ The Attempt at a Solution By taking laplace on the potential I get: ## \rho(\mathbf{r}) =...
14. ### Force at center of cube due to four charges of equal mag.

Homework Statement Four charges of 2*10^-7 are placed on the corners of one face of a cube of 15 cm. A charge of -2 * 10^-7 C is placed at the center of the cube. What is the force on the charge at the center of the cube? Homework Equations F = k q_1*q_2/r^2 3. The Attempt at a Solution...
15. ### I'm making an Arithmetic Error, Electrostatic force diagrams

Homework Statement Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 2.7 cm . Two of the particles have a negative charge: q1 = -6.0 nC and q2 = -12.0 nC. The remaining particle has a positive charge, q3= 8.0 nC . What is the net...