Four charges each Q in magnitude

1. The problem statement, all variables and given/known data
Four charges, each q in magnitude, are arranged in a square, two positive and two negative, in opposite corners. The square is L length on each side, and the charges are all in the same plane as shown in the diagram. Show work and units for full credit.

q+ —–B—– q-
| |
| | L
| |
q- ———— q+
L
**vertical dotted line makes square but spacing corrects itself

A. Determine the magnitude and direction of the total electric field at point B (half way between the top two charges) due to all four charges as a function of q and L.

B. If placed at point B, which would accelerate faster, object 1 with a charge 2Q and mass M or object 2 with a charge Q and mass M/2? Why?

C. Draw the electric field lines in the plane of the square indicating the direction and general shape of the electric field generated by this charge arrangement. Hint: think about the electric field generated by two opposite charges.

D. Is the electric field zero at any point(s)? If so, where? Also, indicate any equilibrium point(s) and whether they are stable, unstable or neutral.

3. The attempt at a solution

A. E=(36/5)(q/L^2)

B. Both are equal a = 2qE/m = qE/(m/2)

D. 0 at top of square going in towards B from + and towards B for –

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