Classical Dynamics of Particles and Systems
5th Edition
ISBN: 9780534408961
Author: Stephen T. Thornton, Jerry B. Marion
Publisher: Cengage Learning
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Describe schematically the equipotential surfaces corresponding to(a) a constant electric field in the z-direction,(b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction,(c) a single positive charge at the origin, and(d) a uniform grid consisting of long equally spaced parallel charged wires in a plane.
Starting with the definition of work, prove that at every point on an equipotential surface, the surface must be perpendicular to the electric field there.
If the plane x = 4 m is an equipotential surface, in which of the following directions can the electric field be in the region immediately adjacent to this plane?
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- Two very large metal plates are placed 2.0 cm apart, with a potential difference of 12 V between them. Consider one plate to be at 12 V, and the other at 0 V. (a) Sketch the equipotential surfaces for 0, 4, 8, and 12 V. (b) Next sketch in some electric field lines, and confirm that they are perpendicular to the equipotential lines.arrow_forwardYou have seen the equipotential lines of a point charge. How do we calculate them? For example, if we have a +10-nC charge at the origin, what are the equipotential surfaces at which the potential is (a) 100 V, (b) 50 V, (c) 20 V, and (d) 10 V?arrow_forwardHello, Though I understand how to calculate the capacitance with dielectic inserted, I have no idea how to deal with problems with partially-filled in dilectrics. Not to mention the work required to remove the dielectric in either battery-connected or battery-disconnected state. Could you please help me explain?arrow_forward
- A particle with charge q=1.4 mC moves 0.40 m along an equipotential surface of 10.0 V. How much work is done by the electric field during this motion? Show all work.arrow_forwardThe electric potential distribution in a certain region of space isgiven by V (z) = (8 V/m^2)z^2 + (5 V/m)z, where the independent variableis in units of m. The equipotential surfaces in this region arearrow_forwardHow do we determine the region(s) with the strongest/weakest electric field usingthe equipotential line plots?arrow_forward
- Which of the following is the potential expression at the center (at the origin) of the half-ring rod that is at its central origin, has a linear charge density ρl, and is located between 0≤ϕ≤2 on the x-y axis?arrow_forwardFind the electric potential at a distance h from the center of a disk of radius R, with a charge distribution homogeneous σarrow_forwardSuppose that we have a conductive sphere to the radius ( a ) containing the specific potential ( v0 ) this sphere we positioned in the center of a charged ring to the radius ( b ) , solve the problem of the total Q loop using the potential images of this system at a point such as P .arrow_forward
- An electron is held at point c. In what direction will it move when released? If it starts from rest, how fast will it be moving when it crosses the equipotential line that point b sits at? (You may need to look up a constant or two.) Answer the same questions, but for a proton placed at point b and eventually crossing c’s equipotential line.arrow_forwardConsider the line of charge shown on the attached figure. If the radius of the arc is R and the linear charge density on the line is λ, find the potential at the point P shown.arrow_forwardUsing the values on the equipotential lines and measuring the distance between them, estimate the magnitude of electric field at three different places for each configuration.arrow_forward
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