Respuesta :
Answer:
2585.34N
Explanation:
Parameters given;
[tex]q_1 = -2.3 * 10^{-6}C\\q_2 = 3.2 * 10^{-6}C\\q_3 = -1.6 * 10^{-6}C\\k = 8.99 * 10^{9}Nm^{2}[/tex]
The total force F acting on [tex]q_2[/tex] is the addition of the force acting on
Taking charge [tex]q_2[/tex] as our reference point, then:
F = [tex]-F_{q_1q_2}[/tex] + [tex]F_{q_2q_3}[/tex]
[tex]F_{q_1q_2}[/tex] is negative because if we take [tex]q_2[/tex] as our reference point (origin), then, [tex]-F_{q_1q_2}[/tex] would be on the -ve x axis.
We have to consider the positions and directions of the forces.
[tex]F_{q_1q_2}[/tex] = [tex]\frac{kq_1q_2}{r^2}[/tex]
r = distance between both charges.
Distance between charge [tex]q_1[/tex] and [tex]q_2[/tex] = 7.5 cm = [tex]7.5 * 10^{-3}[/tex]m
[tex]F_{q_1q_2}[/tex] = [tex]\frac{8.99 * 10^9 * -2.3 * 10^{-6} * 3.2 * 10^{-6}}{(7.5 * 10^{-3})^2}[/tex]
[tex]F_{q_1q_2}[/tex] = -1176.29N
[tex]F_{q_2q_3}[/tex] = [tex]\frac{kq_2q_3}{r^2}[/tex]
Distance between charge [tex]q_2[/tex] and [tex]q_3[/tex] = (11 - 7.5) cm = 3.5cm = [tex]3.5 * 10^{-3}[/tex]m
[tex]F_{q_2q_3}[/tex] = [tex]\frac{9 * 10^9 * 3.2 * 10^{-6} * -1.6 * 10^{-6}}{(3.5 * 10^{-3})^2}[/tex]
[tex]F_{q_2q_3}[/tex] = -3761.63N
Therefore, F is:
[tex]F = -(-1176.29) + (-3761.63)\\\\F = 1176.29 - 3761.63\\\\F = -2585.34N[/tex]
Since we only need the magnitude, F = 2585.34N
The magnitude of force acting on the forces is mathematically given as
F = -2585.34N
What is the magnitude of the force acting on the forces?
Question Parameter(s):
Three-point charges lie on the xx axis.
Charge 1 (-2.3 μCμC ) is at the origin,
charge 2 (+3.2 μCμC ) at xx =7.5 cm
charge 3 (-1.6 μCμC ) is at xx =11 cmcm.
k=8.99×109N⋅m2/C2
Generally, the equation for the total force F is mathematically given as
F = -F{q1q2} + F{q2q3}
Where
F{q1q2} = \frac{kq1q2}{r^2}
[tex]F{q1q2} = \frac{8.99 * 10^9 * -2.3 * 10^{-6} * 3.2 * 10^{-6}}{(7.5 * 10^{-3})^2}[/tex]
F{q1q2} = -1176.29N
Also
[tex]F{q2q3} = \frac{9 * 10^9 * 3.2 * 10^{-6} * -1.6 * 10^{-6}}{(3.5 * 10^{-3})^2}[/tex]
F{q2q3} = -3761.63N
In conclusion
F = -(-1176.29) + (-3761.63)
F = -2585.34N
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