9. (3 points) Compute the electric field vector if the electric potential is V(r

Question

9. (3 points) Compute the electric field vector if the electric potential is V(r,y,22+3ryz. 10. (15 points) Cartesian coordinates are in meters A uniform line charge with total charge Q is on the x axis running from -8,0 to (0,0). (a) Compute the electric field at point P (4,-4). (HINT: What can you do to slightly simplify the computation?) (b) Use this result to determine the electric field at the same point P when another uniform line charge of the same total charge running from (0,-8) to (0,0) is added. Provide exact answers (don't use

Explanation / Answer

9.

The electric field can be given as

Ex= -dV/dx

V= x2+2yz+3xyz

Ex= -dv/dx = -(2x+3yz)= -2x-3yz

Ey= -dv/dy = -(2z+3xz)= -2z-3xy

Ez= -(dV/dz)= -(2y+3xy)= -2y-3xy

E = Exi + Eyj +Ezk

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