An equilateral triangle with sides 2 m each has a charge of 30 μC at each of its three
corners. Determine the electric field at a point 5 m above the center of the triangle.
To determine the electric field at a point 5 m above the center of the triangle, we can use the principle of superposition. This principle states that the electric field at a point due to multiple point charges is the vector sum of the individual electric fields created by each charge.
In this case, we have three charges at the corners of an equilateral triangle. Since the triangle is equilateral, the charges are symmetrically distributed and have the same magnitude (30 μC) at each corner.
To find the electric field at the desired point, follow these steps:
1. Calculate the electric field created by one charge at the desired point.
- The electric field created by a point charge is given by the equation:
E = (k * Q) / r^2
Here, E is the electric field, k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), Q is the charge, and r is the distance between the charge and the point.
- In this case, one charge Q = 30 μC = 30 x 10^-6 C. The distance from the charge to the desired point is the distance from the center of the triangle to the point, which is 5 m.
- Substitute these values into the equation and calculate the electric field created by one charge.
2. Since we have three charges, we need to find the electric field created by each charge and add them as vectors.
- Since the triangle is equilateral, the electric fields created by each charge will have the same magnitude and point radially outward from the center of the triangle.
- To find the total electric field, add the electric fields created by each charge as vectors. Taking into account the geometry, the direction of each field should be 120 degrees apart.
3. Finally, calculate the magnitude and direction of the total electric field at the desired point using the vector sum.
By following these steps, you can determine the electric field at a point 5 m above the center of the equilateral triangle with charges at its corners.