A point charge q = -3.3 micro coulomb is located at the origin of a co-ordinate

Question

A point charge q = -3.3 micro coulomb is located at the origin of a co-ordinate system. Another point charge q2 = 7.1 micro coulomb is located along the x-axis at a distance x2 =6.1 cm from q1. 1) What is F12 , x, the value of the x-component of the force that q1exerts on q2? 2) Charge q2 is now displaced a distance y2= -3.3 cm in the positive y -direction. What is the new value for the x- component of the force that q1 exerts on q2? 3) A third point charge q3 is now positioned halfway between q1 and q2. The net force on q2 now has a magnitude of F2, net = 14.6 N and point away from q1 and q3. What is the value( sign and magnitude) of the charge q3?

Explanation / Answer

a)

Electrostaic force of attraction between 2 charges

F=KQ1Q2/r2

so

F12,x=(9*109)(-3.3*10-6)(7.1*10-6)/0.0612

F12,x=-56.67 N

b)

Distance

r=sqrt[0.0612+0.0332]=0.06935 m

Cos(o)=0.061/sqrt[0.0612+0.0332]=0.8795

The X-component of force is

F12=[KQ1Q2/r2]Cos(o)

F12,x=[(9*109)(-3.3*10-6)(7.1*10-6)/0.069352]*0.8795

F12,x=-38.57 N

c)

Distance from Q1 to Q2 is

r12=sqrt[0.0612+0.0332]=0.06935 m

distance from charge q2 and q3 is

r32=r12/2=0.03468 m

Given

F2,net=14.6 N

F2,net=F12+F32=KQ1Q2/r122+KQ2Q3/r322

14.6=(9*10^9)(-3.3*10-6)(7.1*10-6)/0.069352+(9*109)(7.1*10-6)*Q3/0.034682

Q3=1.1*10-6 C or 1.1 uC

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