Physics Help Please!

Question

Two point charges, Q1 = 3.7 μC and Q2 = -1.3 μC, are placed on the x axis. Suppose that Q2 is placed at the origin, and Q1 is placed at the coordinate x1 = -5.0 cm.

(a) At what point(s) along the x axis is the electric field zero? Determine the x-coordinate(s) of the point(s).
(b) At what point(s) along the x axis is the potential zero? Determine the x-coordinate(s) of the point(s).

Answer 1

For part a)  To locate the zero of the electric field it is useful to consider three intervals of x:

    (-∞ , -5)  ;   (-5, 0) ; (0, ∞)  

   

    For the first interval, the contribution from the positive charge dominates the contribution from the negative charge.  Therefore the zero of the electric field cannot be in this interval.

 

    For the second interval, the fields due to the two charges are in the same direction (to the right).   Therefore the zero of the electric field cannot be in this interval.

 

    This leaves the third interval.   The zero of the electric field is in this interval.   The electric field in this interval is proportional to     3.7/(x + 5)²  - 1.3/ x²    (the positive direction is to the right).   Setting this expression equal to zero and solving for the resulting quadratic equation for x   yields   x = 7.278

 

For part b)   The electric potential is proportional to   3.7 /| x+5|  - 1.3 /  | x |

 

        The absolute values make this equation a bit tricky to solve in algebra.  The simplest approach is to to use a graphing calculator such as the TI-84 to plot this function and then use the 2ndCalc menu to find the zeros.   The two zeros are at x = -1.3   and  x = 2.708.    The value x = -1.3 is very easy to check.

 

It is worth pointing out that the interval approach is needed for the electric field because the electric filed is a vector quantity.    Once the correct interval is found, the algebra is straightforward.    The interval approach is not needed for the potential, because it is a scalar.   However, the algebra is not quite as simple.