A +1.60 nC point charge is placed at one corner of a square (1.00 m on a side), and a -240 nC charge is placed on the corner diagonally opposite. What is the magnitude of the electric field at either of the other two corners?
in simple steps
To find the magnitude of the electric field at either of the other two corners of the square, you can use the formula for the electric field due to a point charge:
Electric field (E) = (k * q) / r^2
Where:
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- q is the charge of the point charge
- r is the distance from the point charge
Step 1: Calculate the distance (r) between the point charge and one of the other corners.
Since the square is 1.00 m on a side, the distance between any two corners is equal to the length of one side of the square. Therefore, r = 1.00 m.
Step 2: Calculate the electric field (E) using the formula.
For the +1.60 nC charge at one corner:
E = (k * q) / r^2
= (9 x 10^9 Nm^2/C^2) * (1.60 x 10^-9 C) / (1.00 m)^2
= 14.4 N/C (rounded to the nearest tenth)
For the -240 nC charge at the diagonally opposite corner, the magnitude of the electric field will be the same since the distance and charge are the same.
Therefore, the magnitude of the electric field at either of the other two corners is 14.4 N/C.
To find the magnitude of the electric field at either of the other two corners of the square, you can follow these steps:
Step 1: Calculate the distance from the A +1.60 nC point charge to each of the other two corners.
- Since it's a square with sides of 1.00 m, the distance to the other corner will also be 1.00 m.
Step 2: Use the Coulomb's Law formula to calculate the electric field magnitude at either of the other two corners.
- Coulomb's Law formula: E = k * q / r^2
- E: Electric field magnitude
- k: Coulomb's constant (9.0 × 10^9 N m^2/C^2)
- q: Charge magnitude
- r: Distance between the charges
Let's assume the distance between the charges is r. Therefore, both r values will be equal to 1.00 m.
Step 3: Calculate the electric field for each corner using Coulomb's Law.
- For the +1.60 nC charge corner:
E1 = (9.0 × 10^9 N m^2/C^2) * (1.60 × 10^-9 C) / (1.00 m)^2
- For the -240 nC charge corner:
E2 = (9.0 × 10^9 N m^2/C^2) * (240 × 10^-9 C) / (1.00 m)^2
Step 4: Simplify the equations and calculate the electric field magnitudes.
- For the +1.60 nC charge corner:
E1 = (9.0 × 10^9 N m^2/C^2) * (1.60 × 10^-9 C) / (1.00)^2
- For the -240 nC charge corner:
E2 = (9.0 × 10^9 N m^2/C^2) * (240 × 10^-9 C) / (1.00)^2
Step 5: Calculate the final values for the electric field magnitudes.
- For the +1.60 nC charge corner:
E1 = 14.4 N/C
- For the -240 nC charge corner:
E2 = -2160 N/C
Therefore, the magnitude of the electric field at either of the other two corners is 14.4 N/C.
To find the magnitude of the electric field at either of the other two corners of the square, we can use the principle of superposition. This principle states that the net electric field at a certain point in space due to multiple charges is the vector sum of the electric fields produced by each individual charge. Here's how you can solve the problem step by step:
Step 1: Calculate the electric field due to the +1.60 nC charge at the desired corner.
- The electric field produced by a point charge is given by the equation: E = k * q / r^2, where E is the electric field, k is the electrostatic constant (9 × 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 find the electric field.
- In this case, the charge q is +1.60 nC, and the distance r is the length of one side of the square, which is 1.00 m.
Step 2: Calculate the electric field due to the -240 nC charge at the desired corner.
- Use the same equation as above, but with the charge q being -240 nC.
Step 3: Add the electric fields obtained in steps 1 and 2 together to find the net electric field at the desired corner.
Step 4: Take the magnitude of the net electric field. Since electric field is a vector quantity, it has both magnitude and direction. However, in this case, we are interested only in the magnitude.
By following these steps, we can determine the magnitude of the electric field at either of the other two corners.