Three charged particles are placed at each of three corners of an equilateral tr

Question

Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 2.1 cm . Two of the particles have a negative charge: q1 = -8.0 nC and q2 = -16.0 nC . The remaining particle has a positive charge, q3 = 8.0 nC . What is the net electric force acting on particle 3 due to particle 1 and particle 2?

A) Find the net force F 3 acting on particle 3 due to the presence of the other two particles. Report you answer as a magnitude F3 and a direction measured from the positive x axis.

Please show the process! I've tried everything I can think of.

Explanation / Answer

step 1:

lets assign coordinates to the corners.

let the bottom two corners are at q1 at (0,0) and q2 at(a,0) where a=2.1 cm

then x coordinate of third corner=a/2 (because perpendicular from one corner to the line joining other two corners bisects the line)

y coordinate=sqrt(3)*a/2 (height of the equilateral triangle=sqrt(3)*length of a side/2)

hence its coordinates are (0.5*a,0.866*a)

now, force on particle 3 due to q1:

as q1 and q3 are of opposite nature, the force will be attractive in anture.

hence it will be away from q3 and towards q1.

direction of force in vector notation=(0,0)-(0.5*a,0.866*a)=(-0.5*a,-0.866*a)

distance=a

so force magnitude=9*10^9*q1*q3/a^2=1.306*10^(-3) N

in vector notation, force=(-0.653,-1.131)*10^(-3) N

now, force on particle 3 due to q2:

as q1 and q3 are of opposite nature, the force will be attractive in anture.

hence it will be away from q3 and towards q2.

direction of force in vector notation=(a,0)-(0.5*a,0.866*a)=(0.5*a,-0.866*a)

distance=a

so force magnitude=9*10^9*q2*q3/a^2=2.6122*10^(-3) N

in vector notation, force=(1.3061,-2.2622)*10^(-3) N

hence net force=(-0.653,-1.131)*10^(-3)+ (1.3061,-2.2622)*10^(-3)=(0.65312,-3.3932)*10^(-3) N

magnitude of force=sqrt(0.65312^2+3.3932^2)*10^(-3)=3.4555*10^(-3) N

direction with +ve x axis=arctan(-3.3932/0.65312)=-79.105 degrees

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