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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 difference V(r) – V(0) for r < a (i.e., where r is inside the insulating sphere, and V(0) is the potential at the origin)?A sphere of radius R centered at the origin carries charge density ρ(r, θ) = k*(R/r^ 2) (R − 2r) sin θ where k is a constant, and r, θ are the usual spherical coordinates. Use the multipole expansion to find the approximate potential for points on the z-axis far from the sphere (z >> R).
- A simple and common technique for accelerating electrons is shown in the figure, which depicts a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to pass through.Randomized VariablesE = 2.7 × 104 N/C Calculate the horizontal component of the electron's acceleration if the field strength is 2.7 × 104 N/C. Express your answer in meters per second squared, and assume the electric field is pointing in the negative x-direction as shown in the figure.Given an electric potential of find its corresponding electric field vector. Sol. Using the concept of potential gradient, we have Since we only have, radial direction (r). Then, the del-operator will be By substitution, we get Evaluating the differential, we, get the following *(q/)Suppose 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 .
- Please answer this, with complete answer An isolated solid spherical conductor of radius 5.00cm is surrounded by dry air. It is given a charge and acquires potential V, with the potential at infinity assumed to be zero. a. Calculate the maximum magnitude can have. b. Explain clearly and concisely why there is a maximum.What is the potential a perpendicular distance of z0 from the center of an annulus (a disk with a hole cut out) with inside radius a, outside radius b, and with a uniform surface charge density σ?Derive this last equation for disk of charge for Potential at point P.
- In Figure 2, there is a positive charge, +q, at point P(d,0,0).At x=0, there is an infinite conducting sheet which is grounded(V=0). At x=3d, there is a constant surface charge densityρs[C/m2] covering whole y-z plane. Dielectric constant isalso ?1 = ?0 for ? > 3?.Hint: Use image theorem.a) Determine the electric field vectors at point C(x,y,z) where ? ∈ (0,3?).Hint: Be careful of what happens at x=3d.b) Determine the electric field vectors at points A(2d,0,0), B(3d-,0,0), B(3d+,0,0).A parrallel plate capacitor has circular cross-section with a radius R and has a charge that varias Q(t). Take the spacing between the plates to be small so that you can assume the electric field is uniform for r < R and vanishes for r>R. Answer in terms of Q(t) and its derivatives.(a) What is the magnitude of the electric field inside the capacitor as a function of time? (b) Inside the capacitor (for r<R), what is the magnetic field as a fucntion of time at a distance r from the center? Use Ampere-Maxwel law with displacement current.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.