Is the dipole potential (given below) a solution to Laplace's equation? Use the Laplacian in spherical coordinates to solve this problem. V (r) = 1 p⋅ cos (0) Απερ r2
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- A spherical water droplet of radius 29 pm carries an excess 234 electrons. What vertical electric field (in N/C) is needed to balance the gravitational force on the droplet at the surface of the earth? (Assume the density of a water droplet is 1,000 kg/m³. Enter the magnitude.)A thin conducting cylindrical shell of radius a, carries a surface charge density o> 0 (the thick- ness of the shell can be neglected). Based on Gauss Law the electric field due to this cylinder is given by SE b) Inside the cylinder r a Determine the corresponding electric potential V(r) as a function of r and relative to a fixed arbitrary reference point A (i.e. rA) for a) Outside the cylinder, at a particular distance r, r > a.1. Consider the Yukawa potential V = g²e T/TO T where r = √√x² + y² + z² and is the distance from the origin and ro is a constant. (This potential arises naturally in nuclear physics but we can imagine it being produced by a specific configuration of electric charge) i) Work in a suitable coordinate system and derive the electric field associated with this potential. ii) Compute the flux through a spherical Gaussian surface centred on the origin as a function of r. iii) Use the above result in the limit that r → ∞ to show that the total charge involved is zero.
- a)What is the magnitude of the electric field at a distance of 0.1 nm from a thorium nucleus? b)What is the magnitude of the force on an electron at that distance? c)Treating the electron classically, that is, as a point object that can move around the nucleus at reasonably slow speeds, what is the frequency of the electron's motion? d)Again treating the electron classically, how fast it it moving? e)What would the magnitude of the force be if the distance of the electron from the nucleus were doubled?A thin plastic rod of length L has a positive charge Q uniformly distributed along its length. We willcalculate the exact field due to the rod in the next homework set. In this set, we will approximatethe rod as several point sources and develop the Riemann sum as an intermediate step on the wayto writing an integral.For those aiming at a P rating, you may use L = 3.0m , Q = 17 mC, and y = 0.11m to calculate theanswer numerically first and substitute variables for them only as required in the problem statement.For those aiming at an E rating, leave L, Q and y as variables. Substitute numbers only whererequired in the problem statement, and only as a last stepPlease don't provide handwritten solution....
- show full and complete procedure. this has to do with the dirac-delta function2) The electric field is given in the form of... E²₁ = ( ( 2 + sin²³0) ^ + (sing cosé @ + 3 =²2 OThis is a challenging problem. Solve it on paper, writing out each step carefully. When doing calculations, do not round intermediate values. Note: If you have approached the problem in a principled way, do not abandon your approach if your numerical answer is not accepted; check your calculations! Four protons (each with mass 1.7 x 10.27 kg and charge 1.6 x 10-19 C) are initially held at the corners of a square that is 5.1 x 10 mon a side. They are then released from rest. What is the speed of each proton when the protons are very far apart? (You may assume that the final speed of each proton is small compared to the speed of light.) Ufinal= m/s