The electric potential in a certain region of space is given by V(x,y,z) = axy +

Question

The electric potential in a certain region of space is given by V(x,y,z) = axy + Beta, in units of volts, where a = 3.22 V/m2 and (3 = 5.58 V are constants. What is the x-component of the electric field at a point P = (3.50, 2.00, 4.00), where the coordinates are given in meters? (in V/m) -9.66||l -7.73||i -6.44 3.22 5.15 6.44 9.66 1.29 times 101 Tries 0/2 What is the magnitude of the electric field at the same point? (in V/m) 7.05 7.96 9.00 1.02 times 101 1. 15 times 101: l.30 times l0l 1.47 times 101 1.66 times 101 Tries 0/2

Explanation / Answer

Electic field = negative gradient of potential

= - (d/dx V) i + (d/dy V) j

= -ay i - ax j

given a is 3.22

=> Electic field = -3.22y i - 3.22x j

Question 1:

given point is (3.50, 2.00, 4.00) => y = 2, x = 3.50

x component of electric field = -3.22 * y = -3.22 * 2 = -6.44 (Option C)

Question 2:

y component of electric field = -3.22 * x = -3.22 * 3.50 = -11.27

therefore, magnitude of the electric field = sqrt(xcomp^2 + ycomp^2)

= sqrt((6.44)^2 + (11.27)^2) = sqrt(168.49) = 12.98 nearly equal to 13 = 1.3 * 10 (option F)

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