Find the components of the electric field at the point (x, y, z) = (3,4,5) of space if the electric potential in that region of space is V(x, y, z) = 2x®y – 3zy +xz². %3D

Solving Poisson's equation V²p=-p /& for the electrostatic potential o(x) in a region with a con charge density po, two students find different answers, viz. Q₁ (x) 1 P₁x² 2 & and 92 (x) = ---P₁²₁ The reason why these different solutions are both correct is because (a) space is isotropic and hence x and y are physically equivalent (b) we can add solutions of Laplace's equation to both (x) and ₂(x) (c) the electrostatic energy is infinite for a constant charge density (d) the boundary conditions are different in the two cases

A spherical conductor has a radius of 14.0 cm and a charge of 62.0 µC. Calculate the electric field and the electric potential at the following distances from the center. (а)r %3D 8.0 сm magnitude MN/C direction electric field there is no direction electric potential there is no direction This would be correct if the charge were located at the origin. MV (b) r = 26.0 cm magnitude direction electric field MN/C ---Select--- electric potential MV ---Select--- (c) r = 14.0 cm magnitude direction electric field 28.47 MN/C outward electric potential 3.98 MV ---Select---

A ring of radius R = 2 cm lies in the y-z plane and is centered at the origin. The ring carries a uniform charge Q = 77 μC. A point P is located along the x-axis a distance x = 2.9 cm from the origin.  a) Calculate the electric potential, in volts, at the point P.   b) Calculate the magnitude of the electric field at the point P in units of meganewtons per coulomb (MN/C)

A flat circular disc of radius R carries a uniform surface charge density o. The potential at a distance z- R² +z² -z. The electric field at z is 2 €0 perpendicularly above the centre of this disk is VR² +z? - z) (9). 2 E, 2z? +R² (a) 2 E0 + R? [H.C.U.-2016] (d) 4 Eo 2z2 + R (c) 4E0 Vz² + R?

a. Determine the magnitude and direction of the electric field at point P, 20 cm away from charge Q =+10µC. Work: Magnitude: N/C Direction:

A conducting spherical shell of radius R and zero thickness is held at a potential V (0) = V, sin* (0). а. Determine the potential produced by the sphere everywhere. b. Determine the electric field produced by the sphere everywhere. C. Determine the surface charge density on the sphere.

2. The magnitude of the electric field at x= +20.0 cm from an infinitely charged plane, located on the y-z plane, is 1.7 x 10³ N/C i. A) What is the charge density on the plane? B) What is the electric potential at x = +20.mem? %3D

15V IDV In the attached pic, equipotential lines with their electric potential values are given 1. Draw the electric field vector at each of the points A, B & C 2. Calculate the change in Electrical Potential Energy when a proton (with positive charge +e) moved from

Determine the electric field intensity and 's) the electric potential at a point P(0, 0, z) for z> 0, due to a rectangular disk of uniform surface charge density Ps = Po[C/m²] as shown in the figure. y=-a x=-b Ꮓ P(0,0,z) y=a x=b Ps = Po[C/m²] x y