The electric potential V(x) for a planar charge distribution is as follows: =(1+²)² =a< x < 0 -Vo(1+²) 0 a V(x) = where V₁ is the potential at the origin and a is a distance. Derive an expression for the corre- sponding electric field Ē(x).
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- The charge density on a disk of radius R = 11.6 cm is given by o = ar, with a = 1.46 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 44.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. V R Ak₂Q Inside a conducting sphere with charge Q and radius R, the electric potential is given by V = the electric field inside and outside the sphere. (Use the following as necessary: ker Q, rand R.) (a) inside E₁ = (b) outside E(r> R) = and outside it is given by V = keq Using Er = dv dr I derive an expression for the magnitude ofGiven is potential V(x,y,z) = 2x2+5y2+6z2-3xyz. where V is in volts and x, y, z are in %3D meters. Find the magnitude of the electric field at point (3,0,2). ( all coordinates in meters) State your answer to the nearest hundredth of the unit. (V/m).
- 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)?The charge density on a disk of radius R = 11.2 cm is given by o = ar, with a = 1.30 μC/m³ and r measured radially outward from the origin (see figure below). What is the electric potential at point A, a distance of 30.0 cm above the disk? Hint: You will need to integrate the nonuniform charge density to find the electric potential. You will find a table of integrals helpful for performing the integration. R A AA 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.