Two equal, positive charges, q=2 microC are locate...

Two equal, positive charges, q=2 microC are located on the xaxis one at +0.3m and the other at -0.3m. A third charge Q=4 microCis located on the y axis at +0.4m.
a.) Find the magnitude and direction of resultant (net force)on Q.
b.) find the electric field and potential at the point(0.0,-0.4m)

Answers ( 1 )

  1. ariana edwards
    ariana edwards
    P     A                     C                B
    Sorry I am not good at drawing But this Fig may help. Let D be the point at y = +0.4 m,
    and x = 0. The third charge Q =4.0 uC is placed at this point, D.
    The el st force on Q exterted by q (placed atat A) isgiven by
                          FQ1 = kq.Q/AD2 along thedirection AD outward.
    Si milary, el st force on Q exterted by q (placedatat B) is given by
                          FQ2 = kq.Q/BD2 along thedirection BD outward.
    These are equal in magnitude.
    To obtain the resultant, we have to find out the angle betweenthem.
    Let the angle DAC = Angle DBC = ?
    Then Tan ? = 0.4/0.3 = 1.333; and ? =tan-1 1.333 = 53.1o
    This is also the angle between the Force vector and and a lineparallel to AB, passing through D.
    To find the resultant we can use parallelogram law orResolution of vectors into rect components.
    Resolving into rect components along the x anf y axes,
    we get, Fcos ? on either side are equal andopposite; so they cancel each other.
    The other components, F sin ? add up, beingalong the same direction.
    The combined force, Fc =2.Fsin ? = 2 kq.Q/AD2 ; AD =0.5 m
    Therefore, Fc =2x9x109x2x4x10-12/x0.5x0.5 = 0.346N
    The direction of Fc is along the y axis
    (b). Potential at the point P (x = -0.4m)
           VP =VP1 +VP2+VP3
              V = kq/r
    where k = 9x109 SIunits, r = 0.1m, 0.7 m an ?(0.42 + 0.42) =?0.32 = 0.566 m respectively
    Substitute and calculate. All terms are positive.
    (c) El field being a vector, the addition is morelengthy.
    For each charge, calculate E =kq/r2 where r has theabove values.
    The directions on of E1 andE2 are are the same along the -ve x axis. Theyadd up.
    The direction of E3 is along DP produced. making an angle? with the x axis; tan ? = 0.4/0.4 = 1. That makes ?= 45 degrees.
    Final combined value of E =?[(E1+E2)2+ E32+2.(E1+E2).E3cos 45]
    The direction, use the formula from parallelogram law.

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