Given a square of sidelength a = 5 cm. We place a charged particle at each corner, three of them carry + 2 nC of charge and one carries the same amount of negative charge.
What is the magnitude of the electric field at the center of the square?
I don't know how to start this problem and would really appreciate it if someone could tell me the method.
Thank you
The center of the square is 5/sqrt2 = 3.535 cm from each corner. The fields due to the two +2nC charges at opposite corners will cancel out. The other two opposite charges will add, and the field will act along the diagonal between them.
Calculate the E field due to the negative charge using Coulomb's Law, and double it to account for the positive charge at the opposite corner.
Is the point charge considered to have a charge of 1?
To find the magnitude of the electric field at the center of the square, you can use the principle of superposition. The electric field at a point is the vector sum of the fields due to each charged particle.
1. Draw a diagram: Start by drawing a square with the given dimensions. Label the positive charges with a "+" and the negative charge with a "-".
2. Calculate the electric field due to each charged particle: To find the electric field at the center of the square, you need to determine the contribution of each particle. The electric field due to a point charge is given by Coulomb's law:
E = (k * q) / r^2
where E is the electric field, k is the Coulomb's constant (8.99 x 10^9 N.m^2/C^2), q is the charge, and r is the distance between the charge and the point where we want to calculate the electric field. You can assume the charges are at the corners of the square.
3. Find the distance to each charge: Since you have a square, you can use the Pythagorean theorem to find the distance from the center to each corner. The distance from the center to any corner is given by a/√2, where a is the length of the sides of the square.
4. Calculate the electric field from each charge: Plug the values into the equation for electric field and calculate the magnitude. Keep in mind that the electric field due to the negative charge will have the opposite sign.
5. Use the principle of superposition: Add up the electric field vectors due to each charge to find the net electric field at the center of the square. Electric fields are vector quantities, so you need to consider their magnitudes and directions.
6. Determine the net electric field magnitude: Once you have the electric fields due to each charge, add them vectorially to find the net electric field at the center of the square. The magnitude of the net electric field is the absolute value of the vector sum.
By following these steps, you should be able to find the magnitude of the electric field at the center of the square.