Homework Problem: Obtain the electric field associated with the following electrostatic potential (Vo and a are constants, the vector potential A = 0): V(r) = V₁ (+44) Vo a
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- Consider a solid insulating sphere which has a total chargeof +3Q but is distributed as ρ(r) = βr, and has a radius of a. This issurrounded by a conducting shell that has a charge of −3Q placed onits outer surface. The inner radius is b and the outer radius is c. a) Determine β in terms of Q and a.b) Find the potential at all points in space1. Find the electric potential at a distance r from the center o of a spherical shell of radius R with charge Q distributed uniformly on the surface of the shell. Consider both cases: r R. Q RA body is charged with a uniform charge density p = 3.1 nC/m³. A spherical cavity is created inside the body with radius R = 0.58 m (all the charges that were inside the sphere were taken out of the body). Before the cavity was created the electric potential at point O (at the center of the cavity) was 40 = 102 V. What is the potential at O after creating the cavity?
- 4. Figure below shows a ring of outer radius R = 13.0 cm, inner radius r= 0.200R, and uniform surface charge density o = 6.20 pC/m2. With V = 0 at infinity, find the electric potential at point P on the central axis of the ring, at distance z = 2.0OR from the center of the ring. %3D Rtion A1 The electric potential V(x) for a planar charge distribution is as follows: (= (1 + 2)² =a a V(x) = where Vo is the potential at the origin and a is a distance. Derive an expression for the corre- sponding electric field Ē(x).A thin circular disc of radius a has a total charge Q uniformly distributed over it. It lies in the x - y plane, centered on the origin. The charge density on the disc is p(F) = e ng² 8(2') for x2 + y2 ≤a² and 0 elsewhere. Calculate (a) the electrostatic potential and (b) the electric field at a general point z on the positive z axis.