A point charge of -4 mu or micro CC is located at x = 4 m, y = -2 m. A second point charge of 12 mu or micro CC is located at x = 1 m, y = 4 m.
SO I took E=Eq1 +Eq2 and got 6967.368 N/C but it is wrong
I agree it is wrong. What I am wondering, with these two charges, where are you determining E? E is a vector.
To calculate the electric field at a specific point due to multiple charges, you need to consider both the magnitudes and directions of the electric fields generated by each charge. The electric field at a point is the vector sum of the individual electric fields at that point.
Let's calculate the electric field at the origin (x = 0, y = 0) due to these two point charges using Coulomb's law:
The electric field due to the first charge (Q1 = -4 μC) at the origin can be calculated as:
E1 = k * |Q1| / r1^2
where k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2), |Q1| is the magnitude of the charge, and r1 is the distance between the point charge and the origin.
For the first charge:
|Q1| = 4 μC = 4 x 10^-6 C
r1 = √((4 - 0)^2 + (-2 - 0)^2) = √(4^2 + (-2)^2) = √(16 + 4) = √20
E1 = (8.99 x 10^9 Nm^2/C^2) * (4 x 10^-6 C) / (√20)^2 = (8.99 x 10^9 Nm^2/C^2) * (4 x 10^-6 C) / 20 = (8.99 x 10^9 Nm^2/C^2) * (4 x 10^-6 C) / 20 = (8.99 x 10^9 Nm^2/C^2) * (4 x 10^-6 C) / 20 = 8.985 x 10^3 N/C
Now, let's calculate the electric field due to the second charge (Q2 = 12 μC) at the origin:
E2 = k * |Q2| / r2^2
where |Q2| = 12 x 10^-6 C and r2 = √((1 - 0)^2 + (4 - 0)^2).
|r2| = √(1^2 + 4^2) = √(1 + 16) = √17
E2 = (8.99 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / (√17)^2 = (8.99 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / 17 = (8.99 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / 17 = (8.99 x 10^9 Nm^2/C^2) * (12 x 10^-6 C) / 17 = 7.222 x 10^3 N/C
To find the total electric field at the origin, we need to calculate the vector sum of E1 and E2:
E = E1 + E2 = (8.985 x 10^3 N/C) + (7.222 x 10^3 N/C) = 16.207 x 10^3 N/C
Therefore, the total electric field at the origin due to these two point charges is 16.207 x 10^3 N/C.
To calculate the electric field at a point due to multiple point charges, you need to consider the contributions from each charge individually. The total electric field at a point is the vector sum of the electric fields created by each charge.
Let's calculate the electric field at a point (x, y) due to the two given charges.
Charge 1: -4 μC located at (4, -2)
Charge 2: 12 μC located at (1, 4)
We will use Coulomb's law to calculate the electric field created by each charge. The electric field created by a point charge Q at a distance r is given by:
E = k * |Q| / r^2
where k is the Coulomb constant (8.99 x 10^9 Nm^2/C^2).
First, let's calculate the electric field created by charge 1 at point P:
Q1 = -4 μC
r1 = distance between charge 1 and point P
Using the distance formula:
r1 = sqrt((x - x1)^2 + (y - y1)^2)
= sqrt((x - 4)^2 + (y - (-2))^2)
Now, calculate |Q1| / r1^2
Q1 / r1^2 = (-4 * 10^-6 C) / [(sqrt((x - 4)^2 + (y + 2)^2))^2]
Next, let's calculate the electric field created by charge 2 at point P:
Q2 = 12 μC
r2 = distance between charge 2 and point P
Using the distance formula:
r2 = sqrt((x - x2)^2 + (y - y2)^2)
= sqrt((x - 1)^2 + (y - 4)^2)
Now, calculate |Q2| / r2^2
Q2 / r2^2 = (12 * 10^-6 C)) / [(sqrt((x - 1)^2 + (y - 4)^2))^2]
Finally, add the contributions from each charge to get the total electric field at point P:
E_total = (k * Q1 / r1^2) + (k * Q2 / r2^2)
Now you can calculate the electric field at any point (x, y) by plugging in the values for Q1, Q2, x, and y into the equation.
Note: Make sure to convert all units to SI units (Coulombs and meters) before performing the calculations.