Trying to make corrections. Thanks a lot! A charge+4 MewC is fixed at the origin

Question

Trying to make corrections. Thanks a lot!

A charge+4 MewC is fixed at the origin, while a charge-1 MewC is on the y-axis at+3 m as shown. What is the resultant electric potential V at the point P on the x axis 4 m from the origin (taking V=0 at infinity)? What is the electric field at point P (express your answer in vector notation)? If you move an electron from infinity to point p, how much work have you done? Express your answer in both eV and Joules. Be careful about signs and explain your logic carefully. A closed Gaussian surface in the shape of edge length 2 m is centered on the origin of the coordinate system (the orientation of the cube is such that the x, y, and z-axis are normal to cube faces). What is the net electric flux through the Gaussian surface?

Explanation / Answer

a) potential is a scalar quantity,

V = kq /d
distance of P from +4uC = 4 m

distance of P from -1uC = sqrt(3^2 + 4^2) = 5 m

V = [ 9 x 10^9 x 4 x 10^-6 / 4 ] + [ 9x 10^-9 x -1 x10^6 / 5 ]

V = 9000 - 1800 = 7200 volt

b) @ = tan^-1(3/4) = 37 deg

due to 4uC:

E1 = kq/d^2 = (9 x 10^9 x 4 x 10^-6 ) / 4^2 (i) = 2250i N/C

due to -1 uC

E2=[ (9 x 10^9 x 1 x10^-6) / 5^2 ] (-cos37i + sin37j)

E2 = - 288i + 216j N/C

Enwt = E1 + E2 = 1960i + 216j

magnitude = sqrt[1960^2 + 216^2] = 1973.85 N/C

direction = tan^-1(216 / 1962) = 6.28 deg

c) Work done = qV = - 1.6 x 10^-19 x 7200 = 1.15 x 10^-15 J

Or - 7200 eV

d) inside cube charge will 4 uC.

and from gauss law,

flux = Qinside / e0 = (4 x 10^-6) / (8.854 x 10^-12) = 451875.28 Wb

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