Question

Relationship Between Electric Potential and Electric Field (easier than it might seem at first glance - follow it step by step) (b) In a given region of space, the electric potential is described by V = (x2 + y2-62)-Volts. i. Determine the equations describing E,i, Eyj,and E,k in this region of space. (5 points) ii. What is the magnitude of the electric field at point P(4m,2m,3m)? (5 points) ii. Recall that for a given function, gx yz), the direction in which g(x.y z) decreases most rapidly from its (의(xwh,J-(剖(x0yM)))-(a (xo yo z)): value at a given point A(xo,yo,zo) is Keeping this in l (xo.yo.zo) mind, whatis the equation of the line along which the electric potential is decreasing most rapidly at point P(4m,2m,3m)? (5 points) (BONUS 5 "extra" points -Do not attempt this part unless you have completed the remainder of the exam) In a "Newtonian, linear approximation the closest point to P(4m,2m 3m) where V = 0V lies on a line that passes, through P(4m,2m,3m) in the direction in which the electric potential is decreasing most rapidly (as found above). Using a parameterization for the line of most rapidly decreasing electric potential, determine the location of the nearest point to P(4m,2m,3m) where V-oV. Work must be showrn for points. You may need the quadratic equation iv. 98

Answer 1

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