Three charges are located on a horizontal axis.
12 µC −0.8 µC 12 µC
p
1.69656 m
2.9 m 2.9 m
Determine the magnitude of the electric
field at p, vertically above the charge −0.8 µC
as shown in the figure. Let up be the positive direction. The Coulomb constant is
8.98755 × 10
9
N · m2
/C
2
.
Answer in units of V/m
To determine the magnitude of the electric field at point P, we can use the principle of superposition. The electric field at P due to each individual charge is calculated separately, and then the results are summed up.
The formula to calculate the electric field produced by a point charge is given by:
E = (k * |q|) / r^2
Where:
E is the electric field
k is the Coulomb constant (8.98755 × 10^9 N · m^2 / C^2)
|q| is the magnitude of the charge
r is the distance between the charge and the point of interest
Let's calculate the electric field at point P due to each charge:
1. The electric field due to the first 12 µC charge:
E1 = (k * |q1|) / r1^2
= (8.98755 × 10^9 N · m^2 / C^2) * (12 × 10^-6 C) / (2.9 m)^2
2. The electric field due to the second -0.8 µC charge:
E2 = (k * |q2|) / r2^2
= (8.98755 × 10^9 N · m^2 / C^2) * (0.8 × 10^-6 C) / (1.69656 m)^2
3. The electric field due to the third 12 µC charge:
E3 = (k * |q3|) / r3^2
= (8.98755 × 10^9 N · m^2 / C^2) * (12 × 10^-6 C) / (2.9 m)^2
Now, we need to calculate the net electric field at point P by summing up the individual electric fields:
E_net = E1 + E2 + E3
Finally, the magnitude of the electric field at point P is given by the absolute value of the net electric field:
|E_net| = |E1 + E2 + E3|
Now, you can plug in the values and calculate the magnitude of the electric field at point P.