Two positive point charges 4.45 mu C are fixed on the y-axis at y = 6.25 mm and

Question

Two positive point charges 4.45 mu C are fixed on the y-axis at y = 6.25 mm and y = -6.25 mm. A negative point charge -3.00 mu C is located 13.0 mm on the +x-axis. What is the x-component of the force on the -3.00 mu C charge? What is the y-component of the force on the -3.00 mu C charge? What is the magnitude of the net force on the -3.00 mu C charge if it is located at the origin? Where must the -3.00 mu C charge be place to obtain the maximum force on it from the 2 charges q? What is that maximum force (magnitude only)?

Explanation / Answer

part 1:

force on -3 uC charge due to charge at y=6.25 mm:

as charges are of opposite sign, force is attractive in nature and directed towards the positive charge.

vector along this direction=(0,6.25)-(13,0)=(-13,6.25)

distance=d1=sqrt(13^26.25^2)=14.4243 mm

unit vector=(-13,6.25)/14.4243=(-0.901256,0.4333)

force magnitude=9*10^9*4.45*10^(-6)*3*10^(-6)/(14.4243*0.001)^2=577.48 N

in vector notation, force=F1=577.48*(-0.901256,0.4333) N

force on -3 uC charge due to charge at y=-6.25 mm:

as charges are of opposite sign, force is attractive in nature and directed towards the positive charge.

vector along this direction=(0,-6.25)-(13,0)=(-13,-6.25)

distance=d1=sqrt(13^26.25^2)=14.4243 mm

unit vector=(-13,-6.25)/14.4243=(-0.901256,-0.4333)

force magnitude=9*10^9*4.45*10^(-6)*3*10^(-6)/(14.4243*0.001)^2=577.48 N

in vector notation, force=F2=577.48*(-0.901256,-0.4333) N

total force=F1+F2=(-1040.9146 ,0) N

so x component of force =-1040.9146 N

part 2:
y component of force =0 N

part 3:

due to symmetr of arrangement , total force will be 0 when -3 uC charge is located at origin.

part 4:

maximum force will be obtained if it is placed very close to one of the charges

such that distance is not zero but close to zero.

as force is inversely proportional to square of distance,

force will be very high when distance is very less.

so ideally answer should be 0 mm.

part 5:

maximum force magnitude will be infinity.

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