A solid, insulating sphere of radius a has a uniform charge density with total charge Q. Concentric with this sphere is an uncharged, conducting shell whose inner and outer radii are b and c (c> b> a). a. Derive ALL the potential fields for 0
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- A conducting sphere of radius a, at potential V0, is surrounded by a thin con- centric ring of radius b and charge Q , The Method of Images ،find potential point P.What is the potential at the center of a disk with a hole cut out of its center with an inside radius a and outside radius b and a surface charge density of d?Using Gauss’s Law and the relation between electric potential and electric field, show that thepotential outside a uniformly charged sphere is identical to the potential of a point charge placed atthe center of the sphere and equal to the total charge of the sphere. (a) What is the potential at thesurface of the sphere? (b) How does the potential change if the charge distribution is not uniform buthas spherical (radial) symmetry?
- Fourpointcharges,eachwithchargeq=+2.0nC,arepositionedequidistantlyaroundacircle of radius r = 5.0 cm as shown in figure (A) below. (a) What is the electric field E at C? (b) What is the potential at point C located at the center (assuming V = 0 infintely far away)? If charge q2 is moved to the same position as q4, as shown in figure (B), what are the new (c) electric field E (d) andpotential at point C?A non-conductive rod has a uniform positive charge density +λ, a total charge Q along its right half, a uniform negative charge density −λ, and a total charge −Q along its left half, see the figure in bellow. (a) What is the electric potential at point A? (b) What is the electric potential at point B?A hollow cylinder of radius r and height h has a total charge q uniformly distributed over its surface. The axis of the cylinder coincides with the z-axis, and the cylinder is centered at the origin, as shown in (Figure 1). What is the potential V0 in the limit as h goes to zero? Express your answer in terms of q, r, and ϵ0. V attached in image 2.
- (a) A sphere has a surface uniformly charged with 1.00 C. At what distance from its center is the potential 5.00 MV? (b) What does your answer imply about the practical aspect of isolating such a large charge?Three particles with equal positive charges q are at the corners of an equilateral triangle of side a as shown. (a) At what point, if any, in the plane of the particles is the electric potential zero? (b) What is the electric potential at the position of one of the particles due to the other two particles in the triangle?Three particles with equal positive charges q are at the corners of an equilateral triangle of side a as shown in the figure below. (a) At what point, if any, in the plane of the particles is the electric potential zero? (b) What is the electric potential at the position of one of the particles due to the other two particles in the triangle? (Use any variable or symbol stated above along with the following as necessary: ke.)V =
- You are given an isolated metal rod of length 3L that carries a uniform charge density ?. Someone is interested in a point ? that is a distance L away from the rod, equidistant from both ends 1) What is the integral you would need to solve to find the total electric field at point P? Answer in terms of ?, ? and ? 2) What is the integral you would need to solve to find the total electric potential at point P? Answer in terms of ?, ? and ? 3) If you connect the bar up to a battery so that a current I now flows through it, what would be an expression for the magnetic field at point P, in terms of ?, ?, ?0The membrane of a living cell can be approximated by a parallel-plate capacitor withplates of area 4.75 * 10-9m2, a plate separation of 8.5 * 10-9m,and a dielectric with a dielectric constant of 4.5. (a) What is theenergy stored in such a cell membrane if the potential differenceacross it is 0.0725 V? (b) Would your answer to part (a) increase,decrease, or stay the same if the thickness of the cell membrane isincreased? ExplainA ring with radius R and a uniformly distributed total charge Q lies in the xy plane, centered at the origin. What is the potential V(z) due to the ring on the z axis as a function of z? What is the magnitude of the electric field E on the z axis as a function of z, for z>0?