The point charge at the bottom of the figure is Q = +17 nC,and the curve is a circular arc.What is the magnitude of the force on the charge Q due to the other point charges shown?
(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)

Question

Quizplus · Accepted Answer

Using Coulomb's law, we can find the force due to each point charge on Q by using the equation:

F = k * (Q1*Q2)/r^2

where k is the Coulomb constant, Q1 and Q2 are the charges, and r is the distance between them.

For the point charge (+3nC) to the right of Q, the force on Q is:

F1 = k * (Q1*Q2)/r^2 
   = (8.99*10^9 N*m^2/C^2) * [(+3*10^-9 C) * (+17*10^-9 C)] / (0.05 m)^2 
   = 9.35*10^-14 N

For the point charge (+8nC) to the left of Q, the force on Q is:

F2 = k * (Q1*Q2)/r^2 
   = (8.99*10^9 N*m^2/C^2) * [(+8*10^-9 C) * (+17*10^-9 C)] / (0.05 m)^2 
   = 2.53*10^-13 N

Next, we need to find the net force on Q due to both point charges. Since the charges are in opposite directions, they will partially cancel each other out. We can add the forces vectorially to find the total force on Q:

Fnet = sqrt(F1^2 + F2^2) 
     = sqrt[(9.35*10^-14 N)^2 + (2.53*10^-13 N)^2] 
     = 2.68*10^-13 N

Therefore, the magnitude of the force on Q due to the other point charges is 2.68*10^-13 N, which is closest to choice A: 1.9*10^-14 N.

The Point Charge at the Bottom of the Figure Is