(a) The value of charge q3 when the total potential is 0, is determined as -1.7 μC.
(b) The value of charge q3 when the total potential is 290 kV, is determined as -0.255 μC.
Electric potential of the charges
The electric potential of a charge at any distance r is calculated as follows;
V = Kq/r
V = k(q₁/r₁ + q₂/r₂ + q₃/r₃)
when the potential, V = 0
0 = k(q₁/r₁ + q₂/r₂ + q₃/r₃)
0 = q₁/r₁ + q₂/r₂ + q₃/r₃
0 = 9.3/4.5 - 4.9/2.9 + q₃/4.5
0 = 0.377 + q₃/4.5
q₃/4.5 = -0.377
q₃ = 4.5 x (-0.377)
q₃ = -1.7 μC
When the potential, V = 290 kV
V = k(q₁/r₁ + q₂/r₂ + q₃/r₃)
290,000 = k(q₁/r₁ + q₂/r₂ + q₃/r₃)
[tex]\frac{290,000}{9\times 10^9} = \frac{9.3 \times 10^{-6}}{0.045} - \frac{4.9\times 10^{-6}}{0.029} + \frac{q_3}{0.029} \\\\3.22 \times 10^{-5} = 2.1 \times 10^{-4} -1.69 \times 10^{-4} + \frac{q_3}{0.029} \\\\3.22 \times 10^{-5} = 4.1 \times 10^{-5} + \frac{q_3}{0.029}\\\\-8.8 \times 10^{-6} = \frac{q_3}{0.029}\\\\q_3 = -2.55 \times 10^{-7}\\\\q_3 = -0.255 \times 10^{-6}\\\\q_3 = -0.255 \ \mu C[/tex]
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