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- Discuss the restrictions on the Gaussian surface used to discuss planar symmetry. For example, is its length important? Does the cross-section have to be square? Must the end faces be on opposite sides of the sheet?arrow_forwardA particle with a charge of -3 x 10-8 C and 2x 10-5 J of kinetic energy enters the regionbetween two charged parallel plates as shownto the right. How far into the region will theparticle travel? If an electron were releasedfrom rest next to the negative plate, with whatspeed would it strike the positive plate?arrow_forwardFigure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise using superposition.arrow_forward
- Determine whether the following vector field is conservative. If it is , find the potential functiona for it. If not demonstrate this. please give specific detailsarrow_forwardRepeat your calculations for the preceding problem, given that the charge is distributed uniformly over the surface of a spherical conductor of radius 10.0 cm.arrow_forwardWhat is the energy required to bring a point charge ? from very far to a distance ? from the center of an insulating sphere of radius ? with charge ?, assuming uniform charge density and d > R? What if the sphere is replaced with a hollow spherical conductor of charge -Q and radius R, what would the energy required be then? Hint: you don’t have to re-derive the potential due to a charged sphere again.arrow_forward
- Find the electric field a distance z above the center of a flat circular disk of radius R (See attatched figure) that carries a uniform surface charge σ. What does your formula give in the limit R → ∞? Also check the case z >> R.arrow_forwardConsider an infinitesimal segment located at an angular position θ on the semicircle, measured from the lower right corner of the semicircle at x=a, y=0. (Thus θ=π2 at x=0, y=a and θ=π at x=−a, y=0.) What are the x- and y- components of the electric field at point P (dEx and dEy) produced by just this segment? Express your answers separated by a comma in terms of some, all, or none of the variables Q, a, θ, dθ, and the constants k and π.arrow_forwardDetermine whether the vector field is conservative and, if so, find the general potential function. F=⟨cos(z),2y^3,−xsin(z)⟩arrow_forward
- Answer the following. Show your complete solution by identifying the givenvariables, unknown , formula , solution, and final answer. A stationary proton is moved from point A, where the potential is 450.0 V, to point B, where the potential is 125 V. (a) How much work is done by the electric force? (b) what is its speed at point B?arrow_forwardPositive charge is distributed with a uniform density λ along the positive x-axis from r to ∞, along the positive y-axis from r to ∞, and along a 90° arc of a circle of radius r, as shown below. What is the electric field at O? (Use the following as necessary: λ, r, and ε0.) E = _____ i + ______ j + ______ karrow_forwardPoint charges are placed at the four corner of a rectangle as shown below: q1=2.0106C , q1=2.0106C , q3=4.0106C and q4=1.0106C . What is the electric field at P ?arrow_forward
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningClassical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning