Three point charges, A = 2.2 µC, B = 7.5 µC, and C = -3.9 µC, are located at the corners of an equilateral triangle as in the figure above. Find the magnitude and direction of the electric field at the position of the 2.2 µC charge.
Using vector addition methods, add the force on A due to B and the force on A due to C. Coulomb's Law will tell you the magnitudes of the forces between pairs.
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To find the magnitude and direction of the electric field at the position of the 2.2 µC charge, we can use the principle of superposition. The electric field at a point due to multiple point charges is the vector sum of the electric fields produced by each individual charge.
Let's first find the electric field at the position of the 2.2 µC charge due to charge A. The magnitude of the electric field E1 at a point due to charge A can be calculated using Coulomb's law:
E1 = (k * |charge A|) / r^2
where k is the electrostatic constant (k = 9 x 10^9 N*m^2/C^2), |charge A| is the magnitude of charge A (2.2 µC = 2.2 x 10^-6 C), and r is the distance between charge A and the position of the 2.2 µC charge.
Next, let's find the electric field at the position of the 2.2 µC charge due to charge B. Similarly, the magnitude of the electric field E2 at a point due to charge B can be calculated using Coulomb's law:
E2 = (k * |charge B|) / r^2
where |charge B| is the magnitude of charge B (7.5 µC = 7.5 x 10^-6 C), and r is the distance between charge B and the position of the 2.2 µC charge.
Finally, let's find the electric field at the position of the 2.2 µC charge due to charge C. The magnitude of the electric field E3 at a point due to charge C can be calculated using Coulomb's law:
E3 = (k * |charge C|) / r^2
where |charge C| is the magnitude of charge C (-3.9 µC = -3.9 x 10^-6 C), and r is the distance between charge C and the position of the 2.2 µC charge.
Now, to get the net electric field at the position of the 2.2 µC charge, we need to calculate the vector sum of the electric fields due to each individual charge:
E_net = E1 + E2 + E3
The magnitude of the net electric field can be calculated as the magnitude of the vector sum of the individual electric fields, and the direction can be determined by finding the angle between the horizontal axis and the direction of the net electric field.