Making the following assumptions: the four charges in the above grid are point c

Question

Making the following assumptions:

the four charges in the above grid are point charges;

each charge has magnitude 1.0 nC (nanocoulombs, and note that two are positive and two are negative);

the grid spacing is 1.0 cm;

all labeled points lie in the same plane as the charges.

1. What are the coordinates of the grid point closest to where the magnitude of the electric field is th smallest? (P,Q,R,S,or T)

2. Determine the magnitude and direction of the electric field at point R (include units).

Magnitude =

Direction, as an angle measured from the + x axis =

Explanation / Answer

1. From the figure you will get that at point P, y component of electric fields made by two +q’s will be minimised by two other –q’s and by the symmetry of two +q’s x component is already balanced. Thus at point P E will have smallest magnitude.

2. In the below figure,

E(+q)= E4 is neutralised by E(-q)=E3

Thus the net E will be by other +q and –q which again are at the same distance from R.

Enet = E1 + E2

E1=E2= kq/(3^2+1^2) = (9*10^9*1*10^-9)/2 = 9/2= 4.5 N/C

= tan^-1(1/3) = 18.43deg

E1x= E1sin= 4.5sin18.43 = 1.42 N/C

E1y= E1cos= 4.5cos18.43 = 4.11 N/C

E2x= E2cos= -4.5cos18.43 = -4.11 N/C

E2y= E2sin= -4.5sin18.43 = -1.42 N/C

Enetx = 1.42 – 4.11= -2.69 N/C

Fnety = 4.11-1.42 = 2.69 N/C

Enet = sqrt(Enetx^2 + Enety^2 ) = sqrt(2.69^2 + 2.69^2) = 3.8 N/C

Direction, = tan^-1(-2.69/2.69) = 45 deg above - X axis or 135 deg counter clockwise from + x axis

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