Yu are given a potential functionv x y z x 4xy 2z2 , Ask an Expert

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You are given a potential function:

V (x, y, z) = x + 4xy + 2z² + 1

(Units are volts and metres).

(a) Find the electric field E(x, y,z) at the origin (0,0, 0) AND at point (2, 2,2). You may leave the answers in (i,j, k) notation without finding magnitude and direction.

(b) Find the potential difference going from (2, 2, 2) to the origin (0, 0,0).

(c) How much work has to be done to move a charge -e (an electron) from (2, 2, 2) to the origin? Express you answer in both electron volts (eV) and in Joules.

Hint: use the potentials, not the electric field, to make it easy!

(d) Does the charge move spontaneously from (2,2,2) to the origin, or is an external force required to push it? Explain why.

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