Please solve. An electron and a proton are physically separated by a distance of

Question

Please solve.

An electron and a proton are physically separated by a distance of 5.292 x 10-11 m in a Hydrogen atom. What is the electric potential energy for this configuration, assuming a zero point at infinite separation? Is this energy positive or negative? An electron is accelerated through a potential difference of +1000V. What is the final speed of the electron, if it is initially at rest? The electric potential in a region of space Ls described by V = 3.5x2-4.5y3. The potential is in volts when x and y are given in meters. What must be the dimensions of the numbers 3.5 and 4.5 to make the equation dimensionally correct. Find the electric field, in unit vector notation, at a point (4, 5) in space. What is the magnitude of the electric field? Consider the electric potential for a point charge, q, along one dimension, which we'll label x. The electric potential a distance x away from the point charge can be given as V = 1/4 pi Calculate the electric field, E, for this potential and then show that you get the same electric field for V = 1/4pi c0 9/x + V0, where V0 is any constant.

Explanation / Answer

1)

U = k*q1*q2/r = 9*10^9*(1.6*10^-19)*(-1.6*10^-19)/(5.292*10^-11) = -4.354*10^-18 J

it's negative...

3)

a)

to balance eq. dimensions of both sides should be V

so,

dimensions of 3.5 = V/m^2

dimension of 4.5 = V/m^3

b)

V = 3.5*4^2-4.5*5^3 = -506.5 V

so,

E = V/r = -506.5/sqrt(4^2+5^2) = -79.102

so,

Ex = 4/sqrt(4^2+5^2)*(-79.102) = -49.415

Ey = 5/sqrt(4^2+5^2)*(-79.102) = -61.768

E = -49.415*i-61.768*j

c

|E| = 79.102 N/C

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