A point charge Q1=-2µC is located at x=0, and a point charge Q2=-8µC is placed at on the x -axis of a cartesian coordinate system.The goal of this problem is to determine the electric field,E(x)=E(x)x^ , at various points along the -axis.
(a)What is E(x) (in N/C) for x -68.0 m ?
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What is E(x) (in N/C) at -0.42 m?
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What is E(x) (in N/C) at 65 m?
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To determine the electric field at various points along the x-axis, we can use the formula for the electric field due to a point charge:
E = k * (Q / r^2)
where E is the electric field in N/C, k is the electric constant (k = 9 x 10^9 Nm^2/C^2), Q is the charge in coulombs, and r is the distance from the charge in meters.
(a) To find E(x) at x = -68.0 m, we need to calculate the distance from the charge Q2 to the point:
r = |-68.0 m - 0 m| = 68.0 m
Now, we can substitute the values into the formula:
E = (9 x 10^9 Nm^2/C^2) * (-8 x 10^-6 C) / (68.0 m)^2
E = -8 x 10^3 N/C
Therefore, the electric field at x = -68.0 m is -8 x 10^3 N/C.
(b) To find E(x) at x = -0.42 m, we need to calculate the distance from the charge Q2 to the point:
r = |-0.42 m - 0 m| = 0.42 m
Now, we can substitute the values into the formula:
E = (9 x 10^9 Nm^2/C^2) * (-8 x 10^-6 C) / (0.42 m)^2
E = -4.45 x 10^6 N/C
Therefore, the electric field at x = -0.42 m is approximately -4.45 x 10^6 N/C.
(c) To find E(x) at x = 65 m, we need to calculate the distance from the charge Q2 to the point:
r = |65 m - 0 m| = 65 m
Now, we can substitute the values into the formula:
E = (9 x 10^9 Nm^2/C^2) * (-8 x 10^-6 C) / (65 m)^2
E = -1.91 x 10^2 N/C
Therefore, the electric field at x = 65 m is approximately -1.91 x 10^2 N/C.