The electric potential in certain space is given as a function of x, y, z to be

Question

The electric potential in certain space is given as a function of x, y, z to be V (x, y, z) = 3x?2y2 V. a) Determine the components Ex and Ey of the electric field in this space. [4 points] b) Calculate the values of electric potential at points A = (1, 0) m and B = (0, 1) m [2 points] c) Calculate work that has to be done by the electric field to move a proton from point A to point B in this space. [4 points]

Explanation / Answer

X+y+z=1 ------------> L1 3x+y-3z=5 ----------> L2 x-2y-5z=10 ---------> L3 L1-L3 (x+y+z)-(x-2y-5z)= 1-10 3y+6z=-9 -----------> L4 L2-3*L1 (3x+y-3z)-3*(x+y+z)=5-3*1 -2y-6z=2 -----------> L5 L4+L5 (3y+6z)+(-2y-6z)=-9+2 ==> y=-7 ------------> L6 replace the value of y in L5 -2*(-7)-6Z=2 14-6z=2 -6z=2-14 -6z=-12 ==> z=2 -------------> L7 replace value of y & z from L6 & L7 in L1 x+(-7)+2=1 x-5=1 ==> x=6 x=6 7=-7 z=2

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