Four point charges are placed at the four corners of a square. Each side of the square has a length L. Find the magnitude of the electric force on q2 due to all three charges q1, q3 and q4 for L = 1 m and q = 1.55 �C.
Answer in units of N
Which q is 1.55 C? All four corners?
drwls, all four q is 1.55C
To calculate the magnitude of the electric force on q2 due to charges q1, q3, and q4 for a square with side length L = 1 m and charge q = 1.55 C, we need to consider the electric forces due to each individual charge.
Step 1: Calculate the electric force between q1 and q2.
The electric force between two charges is given by Coulomb's law:
F = (k * |q1 * q2|) / r^2,
where F is the electric force, k is Coulomb's constant (~8.99 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Since the charges q1 and q2 are placed at opposite corners of the square, the distance between them is the length of the square's diagonal, which can be found using the Pythagorean theorem:
r = sqrt(2 * L^2).
Substituting the values into Coulomb's law:
F1 = (8.99 x 10^9 Nm^2/C^2 * |1.55 C * 1.55 C|) / (sqrt(2 * 1^2))^2.
Step 2: Calculate the electric force between q3 and q2.
Since the charges q3 and q2 are also placed at opposite corners of the square, the distance between them is also given by the diagonal of the square:
r = sqrt(2 * L^2).
Using Coulomb's law:
F3 = (8.99 x 10^9 Nm^2/C^2 * |1.55 C * 1.55 C|) / (sqrt(2 * 1^2))^2.
Step 3: Calculate the electric force between q4 and q2.
The charges q4 and q2 are placed on adjacent corners of the square. The distance between them is equal to the length of a side of the square, which is L:
r = L.
Using Coulomb's law:
F4 = (8.99 x 10^9 Nm^2/C^2 * |1.55 C * 1.55 C|) / (1^2).
Step 4: Add up the individual electric forces:
F = F1 + F3 + F4.
Step 5: Calculate the magnitude of the electric force:
|F| = sqrt(Re(F1 + F3 + F4)^2 + Im(F1 + F3 + F4)^2).
Substitute the calculated values into the equation and evaluate to find the magnitude of the electric force on q2 due to all three charges q1, q3, and q4.
To find the magnitude of the electric force on q2 due to all three charges q1, q3, and q4, we need to consider the contributions from each charge separately and then vector sum them together.
The formula for the electric force between two point charges is given by Coulomb's Law:
F = k * (q1 * q2) / r^2
Where F is the magnitude of the electric force, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Here's how we can calculate the magnitude of the electric force on q2 due to each charge:
1. q1: The distance between q1 and q2 is the length of the diagonal of the square, which can be found using the Pythagorean theorem:
d1 = sqrt(L^2 + L^2) = sqrt(2) L
The electric force between q1 and q2 is:
F1 = k * (q1 * q2) / d1^2
2. q3: The distance between q3 and q2 is L. The electric force between q3 and q2 is:
F3 = k * (q3 * q2) / L^2
3. q4: The distance between q4 and q2 is L. The electric force between q4 and q2 is:
F4 = k * (q4 * q2) / L^2
Now, we can calculate the magnitude of the net electric force on q2 by summing the contributions from each charge:
F_net = sqrt((F1 * cos45)^2 + (F3)^2 + (F4)^2)
Note that we use the cosine of 45 degrees because the charges q1 and q2 are on the diagonal of the square.
Substituting the given values:
L = 1 m
q = 1.55 C
k = 8.99 x 10^9 N m^2/C^2
We can calculate the magnitude of the electric force on q2.