The electric potential in a volume of space is given by V(x, y, z) = x^2 + xy^2

Question

The electric potential in a volume of space is given by V(x, y, z) = x^2 + xy^2 +yz. Determine the electric field in this region at the coordinate (3, 4, 5). Use V = kq/r e_x = partial differential V/partial differential x, E_y = partial differential v/partial differential z to derive the expression for the electric field of a point charge, q. A proton with a speed of 1.23.104 m/s is moving from infinity directly toward a second proton. Assuming that the second proton is fixed in place, find the position where the moving proton stops momentarily before turning around.

Explanation / Answer

r = distance of closest approach

v = initial speed = 12300 m/s

m = mass of proton = 1.67 x 10-27 kg

q = charge on proton = 1.6 x 10-19 C

Using conservation of energy

Kinetic energy of proton at infinity = electric potential energy at closest approach

(0.5) m v2 = k q2/r

(0.5) (1.67 x 10-27) (12300)2 = (9 x 109) (1.6 x 10-19)2/r

r = 1.82 x 10-9 m

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