1. The electric field in a region of space near the origin is given by E(x, y, z) = Eo a (a) Evaluate the curl V x E(x, y, z) (b) Setting V(0, 0,0) = 0, select a path from (0,0,0) to (r, y, 0) and compute V (r, y, 0).
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- I need help in part a and EAnother special case turns out to be of considerable interest. Let's see what the electric field is like near the center of a uniformly charged disk (x small, but not zero, for the reasons just given). Suppose that we are so close to the disk that x is very small (x > x). QIA Show that near the disk E- R1. A charge Q, located at the origin in free space produces a field for which Ez = 1.5 kV/m at point P (-2, 1, -1). а. Find Qo b. Find E at M(2, 3, 5) С. Find E at M(2, 3, 5) in cylindrical coordinates
- An insulating sphere of radius R = 3 cm has positive charge uniformly distributed throughout its entire volume. The electric field at the surface of the sphere has a magnitude of E = 5x107 V/m (a) [3 points] Calculate the volumetric charge density p of the sphere (in C/m3) and Calculate the magnitude of the electric field at a point located atr= 1cm, inside the insulator.Figure 1 shows a configuration of a flat plane and an arbitrary shape, both carrying surfacecharge density of magnitude σ. The arrows show the electric field lines. Are the statementsbelow true or false?a) The flat plane is carrying a negative surface charge density −σ and the arbitrary shape iscarrying a positive surface charge density +σ. Justify your answer.b) Both surfaces are equipotential surfaces. Justify your answer.