Three equal positive point charges of magnitude Q = 8.00ì C are located at three corners of a square of edge length d = 11.8 cm. A negative charge -24.00ì C is placed on the fourth corner. At the position of the negative charge, what is the magnitude of the electric field due to the three positive charges?
2.What is the magnitude of the attractive force on the negative charge?
To find the magnitude of the electric field at the position of the negative charge, we can use the principle of superposition. The electric field at a point is the vector sum of the electric fields due to each individual charge.
1. First, let's calculate the electric field due to a single positive charge. The electric field due to a point charge can be calculated using the formula:
Electric field (E) = (1 / (4πε₀)) * (Q / r²)
where Q is the charge, r is the distance of the point charge from the charge, and ε₀ is the vacuum permittivity constant.
2. Next, calculate the electric field due to each of the three positive charges. Since all the charges and distances are equal, the electric field due to these three charges will also be the same at the position of the negative charge.
3. The total electric field at the position of the negative charge is the vector sum of the electric fields due to each of the three positive charges. Since they are all equal and have the same direction, we can simply multiply the electric field due to a single positive charge by 3:
Total Electric field = 3 * Electric field due to a single charge
Now let's plug in the values to find the electric field at the position of the negative charge:
Electric field due to a single charge:
Q = 8.00ì C
r = distance from the charge to the negative charge (the length of the diagonal of the square, which is given by Pythagoras' theorem: r = √(d² + d²))
ε₀ = 8.854187817 x 10⁻¹² C²/(N·m²)
Calculate the electric field due to a single charge using the formula:
Electric field (E) = (1 / (4πε₀)) * (Q / r²)
Repeat this calculation for each of the three positive charges.
Once you have the electric field due to a single charge, you can then find the total electric field at the position of the negative charge by multiplying it by 3.
For the second question, to find the magnitude of the attractive force on the negative charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is given by:
Force (F) = (1 / (4πε₀)) * ((|Q1| * |Q2|) / r²)
where Q1 and Q2 are the charges, r is the distance between the charges, and ε₀ is the vacuum permittivity constant.
In this case, the negative charge is attracted to each of the positive charges, so we need to calculate the attractive force between the negative charge and each of the positive charges. Since the charges and distances are equal, the attractive force between the negative charge and each of the positive charges will be the same.
Calculate the force between the negative charge and each of the positive charges using Coulomb's Law. Then, add up the forces to find the total attractive force on the negative charge.
first, the negative charge has nothing to do with the E field at that postion.
You can add (as vectors) the three contributions from the three charges.
b) force= Eyoufoundabove*qfromnegativecharge