The Electric field at point P is
......................(i) [ where ]
Let
So, equation (i) can be written as
Now Multiplying both sides with we get
Now the first term in the series we can write as
Similarly, the second term we can write as
Similarly for other terms
And
.................
So,
Or
Or
Proved.
1. Consider an arrangement of N rectangular slits with a distance d between adjacent slits. The...
4. Consider the cylindrical waveguide below, which has an electromagnetic wave propagating in the space between the inner and outer conductors, which is a gap where air exists. The radius of the inner conductor is a, while the inner radius of the outer conductor is b (as shown). The fields in the air-gap have the form E = E0r cos (kz z ωt) B = B0r cos (kz z ωt) where E0 and B0 are constants, r is the radial...
please answer all questions Question 1 5 pts As shown in the figure, an unknown charge is located at the origin and an electron is located at x = +0.2 nm. If the net electric force on a small positive test charge is zero at x = -1.5 nm, what is the magnitude and sign of the unknown charge? unknown charge test charge q electron e X=-1.5 nm x=0 x=+0.2 nm 0 -0.78e 0 +0.78e 0 -0.018e +0.018e +28e The...
1. Consider the case where a liquid is confined between two walls a distance D apart with one wall located at r--D/2 and the other at x- D/2. The walls carry a surface charge density of ? and the liquid has only counter-ions to the surface charge. The Poisson-Boltzman equation (PBE) for this case is where is the electric potential that gives the electric field E- d '/dr, no is the nunber density of counter-ions of valency at x =...
Mahiindra cole Centrale Tutorial Sheet-3 Central forces/SHM PHYSICS-101 Date 150220 1) Let a particle be subject to an attractive central force of the form n where r is the distance between the particle and the centre of the force. Find fn), if all circular orbits are to have identical areal velocities, A 2) For what values of n are circular orbits stable with the potential energy un-Ai where A > 0? 3) A satellite of mass m 2,000 kg is...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Note: This test contains ten questions from chapter 19 to chapter 27. For full credit, you should show all the steps of your numerical answers. No credit would be earned for just circling the right answers. Chapter 19 - Electric Potential and Electric Potential Energy 1. Two point charges are of + 7 uC and - 4 C are held at the corners of a rectangle as shown. The lengths of the sides of rectangle are 0.15 m, and 0.05...
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need background information to answer the questions. The prelab questions are in the 3rd photo. this where we put in the answers, just to give you an idea. Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...